Question

The solution of $(2x-10y^3)\frac{dy}{dx}+y=0$ is

• A. $x{y}^2=2y^5+C$
• B. $y{x}^2=2y^5+C$
• C. $x^2{y}^2=2y^5+C$
• D. $Noneofthese$

Answer 1

Answer: (A)

Given differential equation is $\left(2x-10y^3\right)\frac{dy}{dx}+y=0$
or $\frac{dy}{dx}=\frac{-y}{2x+10y^3}$
or $\frac{dy}{dx}=\frac{2x-10y^3}{-y}=\frac{-2x}{y}+10y^2$
or $\frac{dy}{dx}+\frac{2}{y}x=10y^2$
Compare with linear differential equation
$\frac{dx}{dy}+Px=Q$
I.F $=e^{\int \frac{2}{y}dy}=e^{\log y^2}=y^2$
$\therefore$ Required solution is
$x.y^2\int 10y62.y^{2}dy+C$
or $x\times y^2=10\times \frac{y^5}{5}+C$
or $x{y}^2=2y^5+C$