Internal problem ID [4038]
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]
\[ \boxed {{y^{\prime }}^{2}+a x y^{\prime }=b c \,x^{2}} \]
✓ Solution by Maple
Time used: 0.063 (sec). Leaf size: 53
dsolve(diff(y(x),x)^2+a*x*diff(y(x),x) = b*c*x^2,y(x), singsol=all)
\begin{align*} y \left (x \right ) &= \frac {x^{2} \sqrt {a^{2}+4 b c}}{4}-\frac {a \,x^{2}}{4}+c_{1} \\ y \left (x \right ) &= -\frac {x^{2} \sqrt {a^{2}+4 b c}}{4}-\frac {a \,x^{2}}{4}+c_{1} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.013 (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*}