Internal problem ID [3530]
Book: Ordinary differential equations and their solutions. By George Moseley Murphy.
1960
Section: Various 28
Problem number: 798.
ODE order: 1.
ODE degree: 2.
CAS Maple gives this as type [_quadrature]
Solve \begin {gather*} \boxed {\left (y^{\prime }\right )^{2}+a x y^{\prime }-b c \,x^{2}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.083 (sec). Leaf size: 47
dsolve(diff(y(x),x)^2+a*x*diff(y(x),x) = b*c*x^2,y(x), singsol=all)
\begin{align*} y \relax (x ) = \frac {\left (-a +\sqrt {a^{2}+4 c b}\right ) x^{2}}{4}+c_{1} \\ y \relax (x ) = -\frac {\left (a +\sqrt {a^{2}+4 c b}\right ) x^{2}}{4}+c_{1} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.008 (sec). Leaf size: 59
DSolve[(y'[x])^2+a x y'[x]==b c x^2,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {1}{4} x^2 \left (\sqrt {a^2+4 b c}-a\right )+c_1 \\ y(x)\to -\frac {1}{4} x^2 \left (\sqrt {a^2+4 b c}+a\right )+c_1 \\ \end{align*}