Question

Solve the initial value problem. y'=(y^2)+(2xy)+(x^2)-(1), y(0)=1

Answer 1

Given initial value problem ,

  

or ,

or, ............

Let us make an substitution

Substituting these values in we get ,

Integrating both side we get ,

  

, where c is integration constant .

........

Since so ,

or ,

substituting value of in we get ,

or ,

Hence the required solution is ,

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If you have any doubt or need more clarification at any step please comment .