Question

dy/dx= (x+y+1)^2

Solve the given differential equation by using an appropriate substitution

Answer 1

\[u=x+y+1\]
gives
\[u'=1+y'\]
Subbing into the equation, you have
\[\begin{align*}u'-1&=u^2\\
\frac{du}{u^2-1}&=dx\end{align*}\]

Answer 2

\(u^2\color{red}+1\), sorry.