ques. To solve the differential equation : y - x.dy/dx=a( y²  + x².dy/dx) ; y(a)=a.

Hi!

Here is the answer to your question.

 

 

Comparing the coefficients of x and the constant terms both sides ap = 1 and p + q = 0

 

 

Compare the coefficients of y and the constant terms of both sides, r = 1 and s – ar = 0

∴ s = ar = a

Substring this value in equation (2), you will obtain the solution of the given differential equation.

 

Hope! You got the answer.

Cheers!