Internal problem ID [8758]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 2, linear second order
Problem number: 1178.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _linear, _nonhomogeneous]]
Solve \begin {gather*} \boxed {y^{\prime \prime } x^{2}-2 x y^{\prime }+\left (x^{2}+2\right ) y-\frac {x^{3}}{\cos \relax (x )}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 28
dsolve(x^2*diff(diff(y(x),x),x)-2*x*diff(y(x),x)+(x^2+2)*y(x)-x^3/cos(x)=0,y(x), singsol=all)
\[ y \relax (x ) = x \sin \relax (x ) c_{2}+\cos \relax (x ) x c_{1}+x \left (x \sin \relax (x )+\cos \relax (x ) \ln \left (\cos \relax (x )\right )\right ) \]
✓ Solution by Mathematica
Time used: 0.03 (sec). Leaf size: 57
DSolve[-(x^3*Sec[x]) + (2 + x^2)*y[x] - 2*x*y'[x] + x^2*y''[x] == 0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {1}{2} e^{-i x} x \left (\log \left (1+e^{2 i x}\right )+e^{2 i x} \left (\log \left (1+e^{-2 i x}\right )-i c_2\right )+2 c_1\right ) \\ \end{align*}