Internal problem ID [9508]
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]]
\[ \boxed {x^{2} y^{\prime \prime }-2 y^{\prime } x +\left (x^{2}+2\right ) y=\frac {x^{3}}{\cos \left (x \right )}} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 23
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)
\[ y \left (x \right ) = x \left (\ln \left (\cos \left (x \right )\right ) \cos \left (x \right )+\cos \left (x \right ) c_{1} +\sin \left (x \right ) \left (x +c_{2} \right )\right ) \]
✓ Solution by Mathematica
Time used: 0.081 (sec). Leaf size: 63
DSolve[-(x^3*Sec[x]) + (2 + x^2)*y[x] - 2*x*y'[x] + x^2*y''[x] == 0,y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \frac {1}{2} e^{-i x} x \left (e^{2 i x} \log \left (1+e^{-2 i x}\right )+\log \left (1+e^{2 i x}\right )-i c_2 e^{2 i x}+2 c_1\right ) \]