Find an explicit solution of the given initial - value problem . x ^ 2 * (dy)/(dx) = y - xy , y(- 1) = - 2

The explicit solution is:

The given differential equation is:

We will use separation of variable to solve it.

Given that y(- 1) = - 2.

So the explicit solution is:

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The ODE,

is separable, since we can write

Integrate both sides to get

Solve for y :

Use the initial condition to solve for C :

So the particular solution to the IVP is

  n=   0.0000 - 0.3750 i  

  n=   0.0000 + 0.3750 i

step-by-step explanation:

one of these should be correct