Internal problem ID [8766]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 2, linear second order
Problem number: 1186.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _linear, _nonhomogeneous]]
Solve \begin {gather*} \boxed {x^{2} y^{\prime \prime }-5 x y^{\prime }+8 y-\sin \relax (x ) x^{3}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.003 (sec). Leaf size: 34
dsolve(x^2*diff(diff(y(x),x),x)-5*x*diff(y(x),x)+8*y(x)-sin(x)*x^3=0,y(x), singsol=all)
\[ y \relax (x ) = x^{4} c_{2}+c_{1} x^{2}+\frac {x^{2} \left (\cos \relax (x )+x \left (x \cosineIntegral \relax (x )-\sin \relax (x )\right )\right )}{2} \]
✓ Solution by Mathematica
Time used: 0.012 (sec). Leaf size: 37
DSolve[-(x^3*Sin[x]) + 8*y[x] - 5*x*y'[x] + x^2*y''[x] == 0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {1}{2} x^2 \left (x^2 \text {CosIntegral}(x)+2 c_2 x^2-x \sin (x)+\cos (x)+2 c_1\right ) \\ \end{align*}