Question

Solve initial value problem
x²dy/dx=(4x²-x-2)/(x+1)(y+1) y(1)=0

Answer 1

To solve the given initial value problem, separate the variables and perform integration to find the solution.

Step-by-step explanation:

To solve the initial value problem x²dy/dx=(4x²-x-2)/(x+1)(y+1) y(1)=0, we can start by separating the variables.

1. First, multiply both sides of the equation by (x+1)(y+1).
2. Then, rewrite the equation as (x+1)(y+1)dy = (4x²-x-2)dx.
3. Integrate both sides of the equation.
4. Solve for y by substituting the initial condition y(1) = 0.

After performing these steps, you will find the solution to the initial value problem.