Question

Solution of a differential equation $\frac{dy}{dx}=\frac{2x^{3}y+3x^4+y}{x-x^4}$ is

• A. $x^{2}y+x^3=\frac{y}{x}+C$
• B. $x^{2}y+2x^3=\frac{y}{x}+C$
• C. $x^{2}y+x^3=\frac{2y}{x}+C$
• D. $y+x^3=\frac{y}{x}+C$

Answer 1

The correct option is A $x^{2}y+x^3=\frac{y}{x}+C$

$\begin{array}{cc}xdy-x^{4}dy& =2x^{3}y\cdot dx+3x^{4}dx+ydx\\ & \\ \frac{xdy-ydx}{x^2}& =\frac{2x^{3}y\cdot dx+3x^{4}dx+x^{4}dx}{x^2}\end{array}$

$\begin{array}{c}\int d\left(\frac{y}{x}\right)=\int 2xydx+3x^{2}dx+x^{2}dy\\ \\ \int d\left(\frac{y}{x}\right)=x^{2}y+x^3+c\\ \\ \frac{y}{x}=x^{2}y+x^3+c\end{array}$