Internal problem ID [8757]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 2, linear second order
Problem number: 1177.
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 }-2 x y^{\prime }+\left (x^{2}+2\right ) y-\frac {x^{2}}{\cos \relax (x )}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.005 (sec). Leaf size: 39
dsolve(x^2*diff(diff(y(x),x),x)-2*x*diff(y(x),x)+(x^2+2)*y(x)-x^2/cos(x)=0,y(x), singsol=all)
\[ y \relax (x ) = x \sin \relax (x ) c_{2}+\cos \relax (x ) x c_{1}+x \left (\sin \relax (x ) \ln \relax (x )-\cos \relax (x ) \left (\int \frac {\sin \relax (x )}{x \cos \relax (x )}d x \right )\right ) \]
✓ Solution by Mathematica
Time used: 0.514 (sec). Leaf size: 116
DSolve[-(x^2*Sec[x]) - 2*x*y'[x] + (2 + x^2)*y'[x] + x^2*y''[x] == 0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \int _1^x-\frac {e^{K[2]-\frac {2}{K[2]}} \sec (K[2]) \int _1^{K[2]}e^{\frac {2}{K[1]}-K[1]} K[1]^2dK[1]}{K[2]^2}dK[2]+\int _1^xe^{\frac {2}{K[1]}-K[1]} K[1]^2dK[1] \left (\int _1^x\frac {e^{K[3]-\frac {2}{K[3]}} \sec (K[3])}{K[3]^2}dK[3]+c_2\right )+c_1 \\ \end{align*}