Internal problem ID [3549]
Book: Ordinary differential equations and their solutions. By George Moseley Murphy.
1960
Section: Various 28
Problem number: 819.
ODE order: 1.
ODE degree: 2.
CAS Maple gives this as type [_quadrature]
\[ \boxed {{y^{\prime }}^{2}+\left (a x +y b \right ) y^{\prime }+y a x b=0} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 22
dsolve(diff(y(x),x)^2+(a*x+b*y(x))*diff(y(x),x)+a*b*x*y(x) = 0,y(x), singsol=all)
\begin{align*} y \left (x \right ) = -\frac {a \,x^{2}}{2}+c_{1} \\ y \left (x \right ) = c_{1} {\mathrm e}^{-x b} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.039 (sec). Leaf size: 34
DSolve[(y'[x])^2+(a x+b y[x])y'[x]+a b x y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to c_1 e^{-b x} \\ y(x)\to -\frac {a x^2}{2}+c_1 \\ y(x)\to 0 \\ \end{align*}