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Question Number 67921 Answers: 0 Comments: 0

∫e^(y^2 /2) dy

$$\int{e}^{{y}^{\mathrm{2}} /\mathrm{2}} {dy} \\ $$

Question Number 67920 Answers: 0 Comments: 0

Question Number 67907 Answers: 1 Comments: 1

Question Number 67903 Answers: 2 Comments: 0

Question Number 67902 Answers: 0 Comments: 0

differential equation homogenous. please answer this.with p.s. xydx+2(x^2 +2y^2 )dy=0 x=0 y=1

$${differential}\:{equation} \\ $$$${homogenous}. \\ $$$$ \\ $$$${please}\:{answer}\:{this}.{with}\:{p}.{s}. \\ $$$${xydx}+\mathrm{2}\left({x}^{\mathrm{2}} +\mathrm{2}{y}^{\mathrm{2}} \right){dy}=\mathrm{0} \\ $$$${x}=\mathrm{0} \\ $$$${y}=\mathrm{1} \\ $$

Question Number 67900 Answers: 0 Comments: 0

homogenous differential equation. please answer. y(x^2 +xy−2y^2 )dx+x(3y^2 −xy−x^2 )2y=0 can someone answer this??

$${homogenous}\:{differential}\:{equation}. \\ $$$${please}\:{answer}. \\ $$$${y}\left({x}^{\mathrm{2}} +{xy}−\mathrm{2}{y}^{\mathrm{2}} \right){dx}+{x}\left(\mathrm{3}{y}^{\mathrm{2}} −{xy}−{x}^{\mathrm{2}} \right)\mathrm{2}{y}=\mathrm{0} \\ $$$$ \\ $$$${can}\:{someone}\:{answer}\:{this}?? \\ $$

Question Number 67899 Answers: 1 Comments: 2

homogenous differential equation. (2xy+y^2 )dr−2x^2 dy=0 y=e x=e

$${homogenous}\:{differential}\:{equation}. \\ $$$$ \\ $$$$\left(\mathrm{2}{xy}+{y}^{\mathrm{2}} \right){dr}−\mathrm{2}{x}^{\mathrm{2}} {dy}=\mathrm{0} \\ $$$${y}={e} \\ $$$${x}={e} \\ $$

Question Number 67898 Answers: 0 Comments: 0

differential equation. homogenous. ydx+(2x+3y)dy=0

$$ \\ $$$${differential}\:{equation}. \\ $$$${homogenous}. \\ $$$$ \\ $$$${ydx}+\left(\mathrm{2}{x}+\mathrm{3}{y}\right){dy}=\mathrm{0} \\ $$$$ \\ $$

Question Number 67881 Answers: 1 Comments: 0

find all x,y ∈R such that (x+yi)^(2019) =x−yi

$${find}\:{all}\:{x},{y}\:\in{R}\:{such}\:{that} \\ $$$$\left({x}+{yi}\right)^{\mathrm{2019}} ={x}−{yi} \\ $$

Question Number 67871 Answers: 1 Comments: 1

8=4x x=?

$$\mathrm{8}=\mathrm{4x} \\ $$$$\mathrm{x}=? \\ $$

Question Number 67860 Answers: 1 Comments: 3

Question Number 67852 Answers: 1 Comments: 4

Question Number 67851 Answers: 0 Comments: 5

find ∫ (dx/(x^2 −z)) with z from C .

$${find}\:\int\:\:\frac{{dx}}{{x}^{\mathrm{2}} −{z}}\:\:{with}\:{z}\:{from}\:{C}\:. \\ $$

Question Number 67850 Answers: 0 Comments: 1

calculate ∫_(−∞) ^(+∞) (dx/(x^2 −z)) with z from C

$${calculate}\:\int_{−\infty} ^{+\infty} \:\:\frac{{dx}}{{x}^{\mathrm{2}} −{z}}\:\:{with}\:{z}\:{from}\:{C} \\ $$

Question Number 67849 Answers: 1 Comments: 7

Question Number 67844 Answers: 0 Comments: 2

x^2 +∣x∣−6=0

$${x}^{\mathrm{2}} +\mid{x}\mid−\mathrm{6}=\mathrm{0} \\ $$

Question Number 67836 Answers: 0 Comments: 0

If determinant ((x^n ,x^(n+2) ,x^(n+3) ),(y^n ,y^(n+2) ,y^(n+3) ),(z^n ,z^(n+2) ,z^(n+3) )) = (x−y)(y−z)(z−x)((1/x) + (1/y) + (1/z)), then n equals

$$\mathrm{If}\:\begin{vmatrix}{{x}^{{n}} }&{{x}^{{n}+\mathrm{2}} }&{{x}^{{n}+\mathrm{3}} }\\{{y}^{{n}} }&{{y}^{{n}+\mathrm{2}} }&{{y}^{{n}+\mathrm{3}} }\\{{z}^{{n}} }&{{z}^{{n}+\mathrm{2}} }&{{z}^{{n}+\mathrm{3}} }\end{vmatrix} \\ $$$$=\:\left({x}−{y}\right)\left({y}−{z}\right)\left({z}−{x}\right)\left(\frac{\mathrm{1}}{{x}}\:+\:\frac{\mathrm{1}}{{y}}\:+\:\frac{\mathrm{1}}{{z}}\right), \\ $$$$\mathrm{then}\:{n}\:\mathrm{equals} \\ $$

Question Number 67835 Answers: 1 Comments: 0

∫_0 ^2 x(8−x^3 )^(1/3) dx

$$\int_{\mathrm{0}} ^{\mathrm{2}} {x}\left(\mathrm{8}−{x}^{\mathrm{3}} \right)^{\frac{\mathrm{1}}{\mathrm{3}}} {dx} \\ $$

Question Number 67826 Answers: 2 Comments: 4

Question Number 67823 Answers: 0 Comments: 0

∫_0 ^1 x^(lnx+e^(lnx/x) ) dx

$$\int_{\mathrm{0}} ^{\mathrm{1}} {x}^{{lnx}+{e}^{{lnx}/{x}} } {dx} \\ $$

Question Number 67820 Answers: 0 Comments: 1

x^3 −x^2 −6x

$${x}^{\mathrm{3}} −{x}^{\mathrm{2}} −\mathrm{6}{x} \\ $$

Question Number 67819 Answers: 0 Comments: 1

y=x^5 +ax^4 +bx^3 +cx^2 +dx+e If we let x=t+h can we find h in terms of a,b,c,d,e such that y=(t+R)(t^2 +pt+q)(t^2 +s) this means two roots are of opposite sign, of course its possible by shifting the curve along x, but can we find the shift h ?

$${y}={x}^{\mathrm{5}} +{ax}^{\mathrm{4}} +{bx}^{\mathrm{3}} +{cx}^{\mathrm{2}} +{dx}+{e} \\ $$$${If}\:{we}\:{let}\:{x}={t}+{h} \\ $$$${can}\:{we}\:{find}\:{h}\:{in}\:{terms}\:{of}\:{a},{b},{c},{d},{e} \\ $$$${such}\:{that} \\ $$$${y}=\left({t}+{R}\right)\left({t}^{\mathrm{2}} +{pt}+{q}\right)\left({t}^{\mathrm{2}} +{s}\right) \\ $$$${this}\:{means}\:{two}\:{roots}\:{are}\:{of} \\ $$$${opposite}\:{sign},\:{of}\:{course}\:{its} \\ $$$${possible}\:{by}\:{shifting}\:{the}\:{curve} \\ $$$${along}\:{x},\:{but}\:{can}\:{we}\:{find}\:{the} \\ $$$${shift}\:\boldsymbol{{h}}\:? \\ $$

Question Number 67807 Answers: 1 Comments: 2

Question Number 67799 Answers: 1 Comments: 3

calculate ∫_0 ^∞ (dx/((x^2 −e^(ia) )(x^2 −e^(ib) ))) with a>0 andb>0

$${calculate}\:\int_{\mathrm{0}} ^{\infty} \:\:\frac{{dx}}{\left({x}^{\mathrm{2}} \:−{e}^{{ia}} \right)\left({x}^{\mathrm{2}} −{e}^{{ib}} \right)}\:\:{with}\:{a}>\mathrm{0}\:{andb}>\mathrm{0} \\ $$

Question Number 67795 Answers: 0 Comments: 2

let A_p =∫_0 ^π x^p cos(nx)dx 1) calculate A_0 ,A_1 ,A_2 2)determine a relation of recurrence between A_p

$${let}\:\:{A}_{{p}} =\int_{\mathrm{0}} ^{\pi} \:{x}^{{p}} \:{cos}\left({nx}\right){dx} \\ $$$$\left.\mathrm{1}\right)\:{calculate}\:{A}_{\mathrm{0}} ,{A}_{\mathrm{1}} ,{A}_{\mathrm{2}} \\ $$$$\left.\mathrm{2}\right){determine}\:{a}\:{relation}\:{of}\:{recurrence}\:{between}\:\:{A}_{{p}} \\ $$

Question Number 67775 Answers: 2 Comments: 0

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