29.28.10 problem 808

Internal problem ID [5391]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Various 28
Problem number : 808
Date solved : Monday, January 27, 2025 at 11:17:53 AM
CAS classification : [_quadrature]

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

✓ Solution by Maple

Time used: 0.004 (sec). Leaf size: 25

dsolve(diff(y(x),x)^2+y(x)*diff(y(x),x) = x*(x+y(x)),y(x), singsol=all)
 

\begin{align*} y \left (x \right ) &= \frac {x^{2}}{2}+c_{1} \\ y \left (x \right ) &= 1+{\mathrm e}^{-x} c_{1} -x \\ \end{align*}

✓ Solution by Mathematica

Time used: 0.050 (sec). Leaf size: 32

DSolve[(D[y[x],x])^2+y[x]*D[y[x],x]==x*(x+y[x]),y[x],x,IncludeSingularSolutions -> True]
 

\begin{align*} y(x)\to \frac {x^2}{2}+c_1 \\ y(x)\to -x+c_1 e^{-x}+1 \\ \end{align*}