Internal problem ID [3522]
Book: Ordinary differential equations and their solutions. By George Moseley Murphy.
1960
Section: Various 27
Problem number: 790.
ODE order: 1.
ODE degree: 2.
CAS Maple gives this as type [_quadrature]
Solve \begin {gather*} \boxed {\left (y^{\prime }\right )^{2}+2 y^{\prime } x -3 x^{2}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.002 (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 \relax (x ) = \frac {x^{2}}{2}+c_{1} \\ y \relax (x ) = -\frac {3 x^{2}}{2}+c_{1} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.002 (sec). Leaf size: 29
DSolve[(y'[x])^2+2 x y'[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*}