Internal problem ID [11671]
Book: Differential Equations by Shepley L. Ross. Third edition. John Willey. New Delhi.
2004.
Section: Chapter 2, section 2.3 (Linear equations). Exercises page 56
Problem number: 37 (b).
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_separable]
\[ \boxed {\left (y+1\right ) y^{\prime }+x \left (y^{2}+2 y\right )=x} \]
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 37
dsolve((y(x)+1)*diff(y(x),x)+x*(y(x)^2+2*y(x))=x,y(x), singsol=all)
\begin{align*} y \left (x \right ) &= -1-\sqrt {2+{\mathrm e}^{-x^{2}} c_{1}} \\ y \left (x \right ) &= -1+\sqrt {2+{\mathrm e}^{-x^{2}} c_{1}} \\ \end{align*}
✓ Solution by Mathematica
Time used: 29.843 (sec). Leaf size: 163
DSolve[(y[x]+1)*y'[x]+x*(y[x]^2+2*y[x])==x,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -1-e^{-x^2} \sqrt {e^{x^2} \left (2 e^{x^2}+e^{2 c_1}\right )} \\ y(x)\to -1+e^{-x^2} \sqrt {e^{x^2} \left (2 e^{x^2}+e^{2 c_1}\right )} \\ y(x)\to -1-\sqrt {2} \\ y(x)\to \sqrt {2}-1 \\ y(x)\to \sqrt {2} e^{-x^2} \sqrt {e^{2 x^2}}-1 \\ y(x)\to -\sqrt {2} e^{-x^2} \sqrt {e^{2 x^2}}-1 \\ \end{align*}