64.5.34 problem 37 (b)

Internal problem ID [13347]
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)
Date solved : Tuesday, January 28, 2025 at 05:31:20 AM
CAS classification : [_separable]

\begin{align*} \left (y+1\right ) y^{\prime }+x \left (y^{2}+2 y\right )&=x \end{align*}

✓ Solution by Maple

Time used: 0.011 (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 &= -1-\sqrt {2+{\mathrm e}^{-x^{2}} c_{1}} \\ y &= -1+\sqrt {2+{\mathrm e}^{-x^{2}} c_{1}} \\ \end{align*}

✓ Solution by Mathematica

Time used: 23.612 (sec). Leaf size: 163

DSolve[(y[x]+1)*D[y[x],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*}