29.27.24 problem 790

Internal problem ID [5374]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Various 27
Problem number : 790
Date solved : Monday, January 27, 2025 at 11:17:28 AM
CAS classification : [_quadrature]

\begin{align*} {y^{\prime }}^{2}+2 x y^{\prime }-3 x^{2}&=0 \end{align*}

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 21

dsolve(diff(y(x),x)^2+2*x*diff(y(x),x)-3*x^2 = 0,y(x), singsol=all)
 

\begin{align*} y \left (x \right ) &= \frac {x^{2}}{2}+c_{1} \\ y \left (x \right ) &= -\frac {3 x^{2}}{2}+c_{1} \\ \end{align*}

✓ Solution by Mathematica

Time used: 0.003 (sec). Leaf size: 29

DSolve[(D[y[x],x])^2+2*x*D[y[x],x]-3*x^2==0,y[x],x,IncludeSingularSolutions -> True]
 

\begin{align*} y(x)\to -\frac {3 x^2}{2}+c_1 \\ y(x)\to \frac {x^2}{2}+c_1 \\ \end{align*}