Differential Equation $y’ =e^{x+y} +x^2$

Question

So i was solving book Vinay kumar integral calculus for jee advanced and was stuck along with my friends for a long time on this question: $$y' =e^{x+y} +x^2$$ I tried adding 1 on both sides and putting $x+y=t$ which gave the equation $d(t)/d(x)=e^t+x^2 +1$ but i am stuck on what to do after that .

Answer 1

$$y' =e^{x+y} +x^2$$ Multiply by $-e^{-y}$: $$-e^{-y}y' +x^2e^{-y}=-e^{x} $$ $$(e^{-y})' +x^2e^{-y}=-e^{x} $$ $$t' +x^2t=-e^{x} $$ Where $t=e^{-y}$. Use integrating factor method to solve.