Internal problem ID [9494]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 2, linear second order
Problem number: 1159.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _exact, _linear, _nonhomogeneous]]
\[ \boxed {x^{2} y^{\prime \prime }+y^{\prime } x -y=a \,x^{2}} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 19
dsolve(x^2*diff(diff(y(x),x),x)+x*diff(y(x),x)-y(x)-a*x^2=0,y(x), singsol=all)
\[ y \left (x \right ) = c_{2} x +\frac {a \,x^{2}}{3}+\frac {c_{1}}{x} \]
✓ Solution by Mathematica
Time used: 0.017 (sec). Leaf size: 24
DSolve[-(a*x^2) - y[x] + x*y'[x] + x^2*y''[x] == 0,y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \frac {a x^2}{3}+c_2 x+\frac {c_1}{x} \]