Internal problem ID [8755]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 2, linear second order
Problem number: 1175.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _exact, _linear, _nonhomogeneous]]
Solve \begin {gather*} \boxed {y^{\prime \prime } x^{2}-2 x y^{\prime }-4 y-\sin \relax (x ) x -\left (a \,x^{2}+12 a +4\right ) \cos \relax (x )=0} \end {gather*}
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 33
dsolve(x^2*diff(diff(y(x),x),x)-2*x*diff(y(x),x)-4*y(x)-x*sin(x)-(a*x^2+12*a+4)*cos(x)=0,y(x), singsol=all)
\[ y \relax (x ) = \frac {c_{1}}{x}+x^{4} c_{2}-\frac {a x \cos \relax (x )+2 \sin \relax (x ) a +\sin \relax (x )}{x} \]
✓ Solution by Mathematica
Time used: 0.148 (sec). Leaf size: 33
DSolve[(-4 - 12*a - a*x^2)*Cos[x] - x*Sin[x] - 4*y[x] - 2*x*y'[x] + x^2*y''[x] == 0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {-(2 a+1) \sin (x)-a x \cos (x)+c_2 x^5+c_1}{x} \\ \end{align*}