Internal problem ID [8727]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 1, linear first order
Problem number: 391.
ODE order: 1.
ODE degree: 2.
CAS Maple gives this as type [_quadrature]
\[ \boxed {{y^{\prime }}^{2}+\left (a y+x b \right ) y^{\prime }+y a b x=0} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 22
dsolve(diff(y(x),x)^2+(a*y(x)+b*x)*diff(y(x),x)+a*b*x*y(x) = 0,y(x), singsol=all)
\begin{align*} y \left (x \right ) &= {\mathrm e}^{-a x} c_{1} \\ y \left (x \right ) &= -\frac {b \,x^{2}}{2}+c_{1} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.044 (sec). Leaf size: 34
DSolve[a*b*x*y[x] + (b*x + a*y[x])*y'[x] + y'[x]^2==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to c_1 e^{-a x} \\ y(x)\to -\frac {b x^2}{2}+c_1 \\ y(x)\to 0 \\ \end{align*}