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Question Number 92708 Answers: 1 Comments: 0

solve the differential equations. (a) (x + 3y^2 )(d^2 y/dx^2 ) + 6y ((dy/dx))^2 + 2(dy/dx) + 2 = 0 (b) (2y−x)(d^2 y/dx^2 ) + 2((dy/dx))^2 −2 (dy/dx) + 2 = 0

$$\mathrm{solve}\:\mathrm{the}\:\mathrm{differential}\:\mathrm{equations}. \\ $$$$\:\left(\mathrm{a}\right)\:\left({x}\:+\:\mathrm{3}{y}^{\mathrm{2}} \right)\frac{{d}^{\mathrm{2}} {y}}{{dx}^{\mathrm{2}} }\:+\:\mathrm{6}{y}\:\left(\frac{{dy}}{{dx}}\right)^{\mathrm{2}} \:+\:\mathrm{2}\frac{{dy}}{{dx}}\:+\:\mathrm{2}\:=\:\mathrm{0} \\ $$$$\left(\mathrm{b}\right)\:\left(\mathrm{2}{y}−{x}\right)\frac{{d}^{\mathrm{2}} {y}}{{dx}^{\mathrm{2}} }\:+\:\mathrm{2}\left(\frac{{dy}}{{dx}}\right)^{\mathrm{2}} \:−\mathrm{2}\:\frac{{dy}}{{dx}}\:+\:\mathrm{2}\:=\:\mathrm{0} \\ $$

Question Number 92702 Answers: 2 Comments: 0

y′′+2y′−3y=e^x +e^(2x)

$${y}''+\mathrm{2}{y}'−\mathrm{3}{y}={e}^{{x}} +{e}^{\mathrm{2}{x}} \\ $$

Question Number 92701 Answers: 0 Comments: 3

Question Number 92700 Answers: 0 Comments: 0

∫_(−(π/2)) ^(π/2) ((tan (x^2 )dx)/x) ?

$$\underset{−\frac{\pi}{\mathrm{2}}} {\overset{\frac{\pi}{\mathrm{2}}} {\int}}\:\frac{\mathrm{tan}\:\left({x}^{\mathrm{2}} \right){dx}}{{x}}\:?\: \\ $$

Question Number 92691 Answers: 1 Comments: 3

find x in eq tan^(−1) (x)= cos^(−1) (x)

$$\mathrm{find}\:{x}\:{in}\:{eq}\:\mathrm{tan}^{−\mathrm{1}} \left({x}\right)=\:\mathrm{cos}^{−\mathrm{1}} \left({x}\right) \\ $$

Question Number 92687 Answers: 0 Comments: 0

In a Gregorian calendar, a year finishing with 00 is a leap year if only it′s vintage is divisible by 400. Also, the 1^(st) January 1900 was a Monday. 1\ Show that a year with the vintage finishing with 00 cannot begin on a Sunday 2\ Show that for a person born between 1900−2071, his 28 anniversary will occur on the same day of birth.

$$\mathrm{In}\:\mathrm{a}\:\mathrm{Gregorian}\:\mathrm{calendar},\:\mathrm{a}\:\mathrm{year}\:\mathrm{finishing}\:\mathrm{with} \\ $$$$\mathrm{00}\:\mathrm{is}\:\mathrm{a}\:\mathrm{leap}\:\mathrm{year}\:\mathrm{if}\:\mathrm{only}\:\mathrm{it}'\mathrm{s}\:\mathrm{vintage}\:\mathrm{is}\:\mathrm{divisible} \\ $$$$\mathrm{by}\:\mathrm{400}.\:\mathrm{Also},\:\mathrm{the}\:\mathrm{1}^{\mathrm{st}} \:\mathrm{January}\:\mathrm{1900}\:\mathrm{was}\:\mathrm{a} \\ $$$$\mathrm{Monday}. \\ $$$$\mathrm{1}\backslash\:\mathrm{Show}\:\mathrm{that}\:\mathrm{a}\:\mathrm{year}\:\mathrm{with}\:\mathrm{the}\:\mathrm{vintage}\:\mathrm{finishing}\:\mathrm{with} \\ $$$$\mathrm{00}\:\mathrm{cannot}\:\mathrm{begin}\:\mathrm{on}\:\mathrm{a}\:\mathrm{Sunday} \\ $$$$\mathrm{2}\backslash\:\mathrm{Show}\:\mathrm{that}\:\mathrm{for}\:\mathrm{a}\:\mathrm{person}\:\mathrm{born}\:\mathrm{between}\:\mathrm{1900}−\mathrm{2071}, \\ $$$$\mathrm{his}\:\mathrm{28}\:\mathrm{anniversary}\:\mathrm{will}\:\mathrm{occur}\:\mathrm{on}\:\mathrm{the}\:\mathrm{same} \\ $$$$\mathrm{day}\:\mathrm{of}\:\mathrm{birth}. \\ $$

Question Number 92684 Answers: 1 Comments: 4

Question Number 92682 Answers: 0 Comments: 5

While uninstalling/reinstalling app please use backup/import to keep your saved equation on device. backup: before unintalling import: after reinstalling

$$\mathrm{While}\:\mathrm{uninstalling}/\mathrm{reinstalling}\:\mathrm{app} \\ $$$$\mathrm{please}\:\mathrm{use}\:\mathrm{backup}/\mathrm{import}\:\mathrm{to}\:\mathrm{keep} \\ $$$$\mathrm{your}\:\mathrm{saved}\:\mathrm{equation}\:\mathrm{on}\:\mathrm{device}. \\ $$$$\mathrm{backup}:\:\mathrm{before}\:\mathrm{unintalling} \\ $$$$\mathrm{import}:\:\mathrm{after}\:\mathrm{reinstalling} \\ $$

Question Number 92712 Answers: 0 Comments: 2

find m for fix function f(x)=(((m−1)x+3)/(x−1))

$${find}\:\:\boldsymbol{{m}}\:{for}\:{fix}\:{function} \\ $$$${f}\left({x}\right)=\frac{\left(\boldsymbol{{m}}−\mathrm{1}\right){x}+\mathrm{3}}{{x}−\mathrm{1}} \\ $$

Question Number 92673 Answers: 1 Comments: 2

Show that if 3 prime numbers, all greater than 3, form an arithmetic progression then the common difference of the progression is divisible by 6.

$$\mathrm{Show}\:\mathrm{that}\:\mathrm{if}\:\mathrm{3}\:\mathrm{prime}\:\mathrm{numbers},\:\mathrm{all}\:\mathrm{greater} \\ $$$$\mathrm{than}\:\mathrm{3},\:\mathrm{form}\:\mathrm{an}\:\mathrm{arithmetic}\:\mathrm{progression}\:\mathrm{then}\:\mathrm{the}\:\mathrm{common} \\ $$$$\mathrm{difference}\:\mathrm{of}\:\mathrm{the}\:\mathrm{progression}\:\mathrm{is}\:\mathrm{divisible}\:\mathrm{by}\:\mathrm{6}. \\ $$

Question Number 92668 Answers: 1 Comments: 2

∫_0 ^p (√(x/(c−x))) dx ?

$$\underset{\mathrm{0}} {\overset{\mathrm{p}} {\int}}\:\sqrt{\frac{\mathrm{x}}{\mathrm{c}−\mathrm{x}}}\:\mathrm{dx}\:?\: \\ $$

Question Number 92646 Answers: 0 Comments: 22

Question Number 92626 Answers: 0 Comments: 1

Question Number 92624 Answers: 0 Comments: 0

Question Number 92621 Answers: 0 Comments: 1

Question Number 92619 Answers: 0 Comments: 0

find x in closset interval [ −4,3 ]of function f(x)= 3x−(9/2)sin^(−1) (((x−3)/3))− (1/2)(((x−3)/3))(√(9−(x−3)^2 )) maximum

$$\mathrm{find}\:\mathrm{x}\:\mathrm{in}\:\mathrm{closset}\:\mathrm{interval}\: \\ $$$$\left[\:−\mathrm{4},\mathrm{3}\:\right]\mathrm{of}\:\mathrm{function}\: \\ $$$$\mathrm{f}\left(\mathrm{x}\right)=\:\mathrm{3x}−\frac{\mathrm{9}}{\mathrm{2}}\mathrm{sin}^{−\mathrm{1}} \left(\frac{\mathrm{x}−\mathrm{3}}{\mathrm{3}}\right)− \\ $$$$\frac{\mathrm{1}}{\mathrm{2}}\left(\frac{\mathrm{x}−\mathrm{3}}{\mathrm{3}}\right)\sqrt{\mathrm{9}−\left(\mathrm{x}−\mathrm{3}\right)^{\mathrm{2}} } \\ $$$$\mathrm{maximum} \\ $$

Question Number 92608 Answers: 0 Comments: 4

Question Number 92605 Answers: 1 Comments: 4

If ((1+x)/(1+(√(1+x)))) +((1−x)/(1−(√(1−x)))) =1 find x

$${If}\:\frac{\mathrm{1}+{x}}{\mathrm{1}+\sqrt{\mathrm{1}+{x}}}\:+\frac{\mathrm{1}−{x}}{\mathrm{1}−\sqrt{\mathrm{1}−{x}}}\:=\mathrm{1} \\ $$$${find}\:{x} \\ $$

Question Number 92635 Answers: 0 Comments: 9

Question Number 92597 Answers: 0 Comments: 1

If f(x)=(1/(x−1)) and g(x)=(√x) find domain and range of g(f(x)) .

$$\mathrm{If}\:\mathrm{f}\left(\mathrm{x}\right)=\frac{\mathrm{1}}{\mathrm{x}−\mathrm{1}}\:\mathrm{and}\:\mathrm{g}\left(\mathrm{x}\right)=\sqrt{\mathrm{x}}\: \\ $$$$\mathrm{find}\:\mathrm{domain}\:\mathrm{and}\:\mathrm{range}\:\mathrm{of}\: \\ $$$$\mathrm{g}\left(\mathrm{f}\left(\mathrm{x}\right)\right)\:. \\ $$

Question Number 92594 Answers: 0 Comments: 5

Question Number 92593 Answers: 0 Comments: 0

using the squeeze theorem show that lim_(x→a) (√x) = (√a)

$$\mathrm{using}\:\mathrm{the}\:\mathrm{squeeze}\:\mathrm{theorem}\: \\ $$$$\mathrm{show}\:\mathrm{that} \\ $$$$\:\:\underset{{x}\rightarrow{a}} {\mathrm{lim}}\:\sqrt{{x}}\:=\:\sqrt{{a}}\: \\ $$

Question Number 92585 Answers: 0 Comments: 1

sin 2z + 5(sin z+cos z)+1=0

$$\mathrm{sin}\:\mathrm{2z}\:+\:\mathrm{5}\left(\mathrm{sin}\:\mathrm{z}+\mathrm{cos}\:\mathrm{z}\right)+\mathrm{1}=\mathrm{0} \\ $$

Question Number 92577 Answers: 1 Comments: 3

lim_(x→∞) ((ln x)/x)

$$\underset{{x}\rightarrow\infty} {\mathrm{lim}}\:\frac{\mathrm{ln}\:\mathrm{x}}{\mathrm{x}} \\ $$

Question Number 92575 Answers: 0 Comments: 6

hello i see a lot of questions about special functions in the forum so this book is a good book to learn special functions for anyone want to learn

$${hello}\: \\ $$$${i}\:{see}\:{a}\:{lot}\:{of}\:{questions}\:{about}\:{special} \\ $$$${functions}\:{in}\:{the}\:{forum}\:{so}\:{this}\:{book} \\ $$$${is}\:{a}\:{good}\:{book}\:{to}\:{learn}\:{special}\:{functions} \\ $$$${for}\:{anyone}\:{want}\:{to}\:{learn} \\ $$

Question Number 92566 Answers: 0 Comments: 2

Posting Question with Images Preferably you should type the question. However if you are using pictures then please do the following steps which posting a photo of printed question. A. Use camscanner app to take pictures (search for camscanner in playstore). B. Crop picture so that you only have specifc question that you want to ask in the image.

$$\mathrm{Posting}\:\mathrm{Question}\:\mathrm{with}\:\mathrm{Images} \\ $$$$\mathrm{Preferably}\:\mathrm{you}\:\mathrm{should}\:\mathrm{type}\:\mathrm{the}\:\mathrm{question}. \\ $$$$\mathrm{However}\:\mathrm{if}\:\mathrm{you}\:\mathrm{are}\:\mathrm{using}\:\mathrm{pictures}\:\mathrm{then} \\ $$$$\mathrm{please}\:\mathrm{do}\:\mathrm{the}\:\mathrm{following}\:\mathrm{steps} \\ $$$$\mathrm{which}\:\mathrm{posting}\:\mathrm{a}\:\mathrm{photo}\:\mathrm{of}\:\mathrm{printed} \\ $$$$\mathrm{question}. \\ $$$$\mathrm{A}.\:\mathrm{Use}\:\mathrm{camscanner}\:\mathrm{app}\:\mathrm{to}\:\mathrm{take}\: \\ $$$$\mathrm{pictures}\:\left(\mathrm{search}\:\mathrm{for}\:\mathrm{camscanner}\:\mathrm{in}\right. \\ $$$$\left.\mathrm{playstore}\right).\: \\ $$$$\mathrm{B}.\:\mathrm{Crop}\:\mathrm{picture}\:\mathrm{so}\:\mathrm{that}\:\mathrm{you}\:\mathrm{only} \\ $$$$\mathrm{have}\:\mathrm{specifc}\:\mathrm{question}\:\mathrm{that}\:\mathrm{you}\:\mathrm{want} \\ $$$$\mathrm{to}\:\mathrm{ask}\:\mathrm{in}\:\mathrm{the}\:\mathrm{image}. \\ $$$$ \\ $$

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