Question

\( \begin{array}{l}\frac{y d y}{x d x}=\sqrt{1+x^{2}+y^{2}+x^{2} y^{2}} \\ x(1-y) d x+\left(1+y^{2}\right)(x-1) d y=0 \\ \frac{d y}{d x}=e^{x+y}+x^{2} e^{y}\end{array} \)

          \( \begin{array}{l}\frac{y d y}{x d x}=\sqrt{1+x^{2}+y^{2}+x^{2} y^{2}} \\ x(1-y) d x+\left(1+y^{2}\right)(x-1) d y=0 \\ \frac{d y}{d x}=e^{x+y}+x^{2} e^{y}\end{array} \)

(y d y)/(x d x)=√(1+x^2+y^2+x^2 y^2)
x(1-y) d x+(1+y^2)(x-1) d y=0
(d y)/(d x)=e^x+y+x^2 e^y

Added by Samah

Differential Equations

E. RUKMANGADACHARI 2012 Edition

Chapter 2

Instant Answer

Solved by Expert Urvashi Arora

08/20/2021

Step 1

The first differential equation is a homogeneous equation of the first order. We can solve it by substituting \(y = vx\), where \(v\) is a function of \(x\). This will transform the equation into a separable equation which can be solved by integration. Show more…

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