29.27.15 problem 781

Internal problem ID [5365]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Various 27
Problem number : 781
Date solved : Monday, January 27, 2025 at 11:17:22 AM
CAS classification : [[_1st_order, _with_linear_symmetries], _Clairaut]

\begin{align*} {y^{\prime }}^{2}+x y^{\prime }-y&=0 \end{align*}

✓ Solution by Maple

Time used: 0.035 (sec). Leaf size: 17

dsolve(diff(y(x),x)^2+x*diff(y(x),x)-y(x) = 0,y(x), singsol=all)
 

\begin{align*} y \left (x \right ) &= -\frac {x^{2}}{4} \\ y \left (x \right ) &= c_{1} \left (x +c_{1} \right ) \\ \end{align*}

✓ Solution by Mathematica

Time used: 0.007 (sec). Leaf size: 23

DSolve[(D[y[x],x])^2+x*D[y[x],x]-y[x]==0,y[x],x,IncludeSingularSolutions -> True]
 

\begin{align*} y(x)\to c_1 (x+c_1) \\ y(x)\to -\frac {x^2}{4} \\ \end{align*}