Internal problem ID [8998]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 2, linear second order
Problem number: 1419.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
Solve \begin {gather*} \boxed {y^{\prime \prime }+\frac {\left (x^{2} \sin \relax (x )-2 \cos \relax (x ) x \right ) y^{\prime }}{x^{2} \cos \relax (x )}+\frac {\left (2 \cos \relax (x )-\sin \relax (x ) x \right ) y}{x^{2} \cos \relax (x )}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.062 (sec). Leaf size: 13
dsolve(diff(diff(y(x),x),x) = -(sin(x)*x^2-2*cos(x)*x)/x^2/cos(x)*diff(y(x),x)-(2*cos(x)-x*sin(x))/x^2/cos(x)*y(x),y(x), singsol=all)
\[ y \relax (x ) = c_{1} x +x \sin \relax (x ) c_{2} \]
✗ Solution by Mathematica
Time used: 0.0 (sec). Leaf size: 0
DSolve[y''[x] == -((Sec[x]*(2*x*Cos[x] - x*Sin[x])*y[x])/x^2) - (Sec[x]*(-2*x*Cos[x] + x^2*Sin[x])*y'[x])/x^2,y[x],x,IncludeSingularSolutions -> True]
Not solved