Internal problem ID [8880]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 2, linear second order
Problem number: 1301.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _exact, _linear, _homogeneous]]
Solve \begin {gather*} \boxed {\left (a \,x^{2}+x b \right ) y^{\prime \prime }+2 y^{\prime } b -2 a y=0} \end {gather*}
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 22
dsolve((a*x^2+b*x)*diff(diff(y(x),x),x)+2*b*diff(y(x),x)-2*a*y(x)=0,y(x), singsol=all)
\[ y \relax (x ) = \frac {c_{1}}{x}+\frac {c_{2} \left (a x +b \right )^{3}}{x} \]
✓ Solution by Mathematica
Time used: 0.017 (sec). Leaf size: 30
DSolve[-2*a*y[x] + 2*b*y'[x] + (b*x + a*x^2)*y''[x] == 0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {\frac {c_2 (a x+b)^3}{a}+3 c_1}{3 x} \\ \end{align*}