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Differential EquationQuestion and Answers: Page 1

Question Number 227855 Answers: 0 Comments: 1

Question Number 227273 Answers: 1 Comments: 0

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Question Number 227250 Answers: 1 Comments: 0

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Question Number 227222 Answers: 2 Comments: 0

Solve x(dy/dx)+y=x^3 6/1/2026

$$\:\:\:\:{Solve} \\ $$$$\:\:\:\:\:\:\:{x}\frac{{dy}}{{dx}}+{y}={x}^{\mathrm{3}} \\ $$$$\:\:\:\:\:\:\mathrm{6}/\mathrm{1}/\mathrm{2026} \\ $$$$ \\ $$

Question Number 227221 Answers: 1 Comments: 0

Solve (x^2 +xy)(dy/dx)=xy−y^2 6/1/2026

$${Solve}\:\:\: \\ $$$$\:\:\:\:\:\:\:\:\left({x}^{\mathrm{2}} +{xy}\right)\frac{{dy}}{{dx}}={xy}−{y}^{\mathrm{2}} \\ $$$$\:\:\:\:\:\:\:\:\mathrm{6}/\mathrm{1}/\mathrm{2026} \\ $$

Question Number 227220 Answers: 2 Comments: 0

Solve (dy/dx)=((x^2 +y^2 )/(xy)) 6/1/2026

$${Solve}\: \\ $$$$\:\:\:\:\:\:\:\frac{{dy}}{{dx}}=\frac{{x}^{\mathrm{2}} +{y}^{\mathrm{2}} }{{xy}} \\ $$$$\:\:\:\:\mathrm{6}/\mathrm{1}/\mathrm{2026} \\ $$

Question Number 227219 Answers: 1 Comments: 0

Solve (dy/dx)=((y^2 +xy^2 )/(x^2 y−x^2 )) 6/1/2026

$${Solve}\: \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\frac{{dy}}{{dx}}=\frac{{y}^{\mathrm{2}} +{xy}^{\mathrm{2}} }{{x}^{\mathrm{2}} {y}−{x}^{\mathrm{2}} } \\ $$$$\:\:\:\:\mathrm{6}/\mathrm{1}/\mathrm{2026} \\ $$$$ \\ $$

Question Number 227173 Answers: 1 Comments: 0

If y−2x(dy/dx)=x(x+1)y^3 Prove that 4/1/2026 y^2 =((6x)/(2x^3 +3x^2 +A))

$$\boldsymbol{{If}}\:\boldsymbol{{y}}−\mathrm{2}\boldsymbol{{x}}\frac{\boldsymbol{{dy}}}{\boldsymbol{{dx}}}=\boldsymbol{{x}}\left(\boldsymbol{{x}}+\mathrm{1}\right)\boldsymbol{{y}}^{\mathrm{3}} \\ $$$${Prove}\:{that}\:\:\:\:\:\:\:\:\:\:\:\:\mathrm{4}/\mathrm{1}/\mathrm{2026} \\ $$$$\:\:\:\:\:\:\:\:\:\:\:{y}^{\mathrm{2}} =\frac{\mathrm{6}{x}}{\mathrm{2}{x}^{\mathrm{3}} +\mathrm{3}{x}^{\mathrm{2}} +{A}} \\ $$

Question Number 227075 Answers: 1 Comments: 0

Question Number 227074 Answers: 1 Comments: 0

Question Number 226898 Answers: 0 Comments: 0

Reduce to canonical form: sin^2 (x)(∂^2 u/∂x^2 )+sin^2 (2x)(∂^2 u/(∂x∂y))+cos^2 (x)(∂^2 u/∂y^2 )=0

$$\mathrm{Reduce}\:\mathrm{to}\:\mathrm{canonical}\:\mathrm{form}: \\ $$$$\mathrm{sin}^{\mathrm{2}} \left(\mathrm{x}\right)\frac{\partial^{\mathrm{2}} \mathrm{u}}{\partial\mathrm{x}^{\mathrm{2}} }+\mathrm{sin}^{\mathrm{2}} \left(\mathrm{2x}\right)\frac{\partial^{\mathrm{2}} \mathrm{u}}{\partial\mathrm{x}\partial\mathrm{y}}+\mathrm{cos}^{\mathrm{2}} \left(\mathrm{x}\right)\frac{\partial^{\mathrm{2}} \mathrm{u}}{\partial\mathrm{y}^{\mathrm{2}} }=\mathrm{0} \\ $$

Question Number 226961 Answers: 1 Comments: 0

σ = ∫_0 ^( ∞) xe^(−x) J_2 (x)dx=?

$$\:\:\: \\ $$$$\:\:\:\:\:\sigma\:=\:\int_{\mathrm{0}} ^{\:\infty} {xe}^{−{x}} \:{J}_{\mathrm{2}} \left({x}\right){dx}=? \\ $$$$\:\:\:\: \\ $$

Question Number 226778 Answers: 0 Comments: 0

Solve the following D.E (a) (dy/dx)+2y=xy^2 (b) (dy/dx)+3(y/x)=2x^4 y^4

$${Solve}\:{the}\:{following}\:{D}.{E} \\ $$$$\left({a}\right)\:\frac{{dy}}{{dx}}+\mathrm{2}{y}={xy}^{\mathrm{2}} \\ $$$$\left({b}\right)\:\frac{{dy}}{{dx}}+\mathrm{3}\frac{{y}}{{x}}=\mathrm{2}{x}^{\mathrm{4}} {y}^{\mathrm{4}} \\ $$

Question Number 226777 Answers: 4 Comments: 0

Show that ∫_0 ^1 x^2 (1+x^2 )^(−1) dx=((4−π)/4) Hence by using Simpson^′ s rule find the value of π with eleven ordinates. correct to 4 decimal places

$${Show}\:{that} \\ $$$$\:\int_{\mathrm{0}} ^{\mathrm{1}} {x}^{\mathrm{2}} \left(\mathrm{1}+{x}^{\mathrm{2}} \right)^{−\mathrm{1}} {dx}=\frac{\mathrm{4}−\pi}{\mathrm{4}} \\ $$$${Hence}\:{by}\:{using}\:{Simpson}^{'} {s} \\ $$$${rule}\:{find}\:{the}\:{value}\:\:{of}\:\pi\:{with}\: \\ $$$${eleven}\:{ordinates}. \\ $$$${correct}\:{to}\:\mathrm{4}\:{decimal}\:{places} \\ $$

Question Number 226732 Answers: 2 Comments: 0

Question Number 224335 Answers: 1 Comments: 0

Question Number 224036 Answers: 0 Comments: 0

(dy/dx)=((y^6 −2x^2 )/(2xy^5 +x^2 y^2 ))

$$\:\frac{{dy}}{{dx}}=\frac{{y}^{\mathrm{6}} −\mathrm{2}{x}^{\mathrm{2}} }{\mathrm{2}{xy}^{\mathrm{5}} +{x}^{\mathrm{2}} {y}^{\mathrm{2}} } \\ $$

Question Number 224025 Answers: 0 Comments: 0

Resuelve la ecuacio^ n diferencial [4x^3 y − (e^(xy) /x) + y ln(x) + x ((x − 4))^(1/3) ]dx + [x^4 − (e^(xy) /y) + x ln(x) − x]dy Help ....

$${Resuelve}\:{la}\:{ecuaci}\acute {{o}n}\:{diferencial} \\ $$$$\left[\mathrm{4}{x}^{\mathrm{3}} {y}\:−\:\frac{{e}^{{xy}} }{{x}}\:+\:{y}\:\mathrm{ln}\left({x}\right)\:+\:{x}\:\sqrt[{\mathrm{3}}]{{x}\:−\:\mathrm{4}}\right]{dx}\:+\:\left[{x}^{\mathrm{4}} −\:\frac{{e}^{{xy}} }{{y}}\:+\:{x}\:\mathrm{ln}\left({x}\right)\:−\:{x}\right]{dy} \\ $$$${Help}\:.... \\ $$

Question Number 223988 Answers: 0 Comments: 0

Solve the DE using the method of Frobenius : (1−x^2 )y′′−2xy′+n(n+1)y=0

$$\mathrm{Solve}\:\mathrm{the}\:\mathrm{DE}\:\mathrm{using}\:\mathrm{the}\:\mathrm{method}\:\mathrm{of}\:\mathrm{Frobenius}\::\: \\ $$$$\left(\mathrm{1}−\mathrm{x}^{\mathrm{2}} \right)\mathrm{y}''−\mathrm{2xy}'+\mathrm{n}\left(\mathrm{n}+\mathrm{1}\right)\mathrm{y}=\mathrm{0} \\ $$

Question Number 223054 Answers: 0 Comments: 0

find y y^dy = x^dx

$$\mathrm{find}\:{y} \\ $$$${y}^{{dy}} =\:{x}^{{dx}} \\ $$

Question Number 222296 Answers: 0 Comments: 0

(1+x^4 )y′−x^3 y = x^5 −x^3 +2x+1

$$\left(\mathrm{1}+{x}^{\mathrm{4}} \right){y}'−{x}^{\mathrm{3}} {y}\:=\:{x}^{\mathrm{5}} −{x}^{\mathrm{3}} +\mathrm{2}{x}+\mathrm{1} \\ $$

Question Number 221973 Answers: 1 Comments: 0

(d^2 y/dx^2 )+y=k−(1/x^2 )−(6/x^4 ) Find y(x) (k is constant).

$$\frac{{d}^{\mathrm{2}} {y}}{{dx}^{\mathrm{2}} }+{y}={k}−\frac{\mathrm{1}}{{x}^{\mathrm{2}} }−\frac{\mathrm{6}}{{x}^{\mathrm{4}} }\:\:\:\:\:\: \\ $$$${Find}\:{y}\left({x}\right)\:\:\:\:\left({k}\:{is}\:{constant}\right). \\ $$

Question Number 218396 Answers: 0 Comments: 0

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