Solve each of the following initial value problems dy/dx = (y(x + 2y))/(x(2x + y)), y(1) = 2

Question

Solve each of the following initial value problems

\(\frac{dy}{dx}=\frac{y(x + 2y)}{x(2x + y)},\,y(1) = 2\)

Answer 1

It is a homogeneous equation

Put y = vx

So,

Comparing the coefficient of like power of v,

A = – 2

A + B = 1

– 2 + B = 1

B = 3

Using in eq. (1)