Internal problem ID [9012]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 2, linear second order
Problem number: 1433.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _linear, _nonhomogeneous]]
Solve \begin {gather*} \boxed {y^{\prime \prime }+\frac {y^{\prime } \sin \relax (x )}{\cos \relax (x )}+\frac {\left (2 x^{2}+x^{2} \left (\sin ^{2}\relax (x )\right )-24 \left (\cos ^{2}\relax (x )\right )\right ) y}{4 x^{2} \cos \relax (x )^{2}}-\left (\sqrt {\cos }\relax (x )\right )=0} \end {gather*}
✓ Solution by Maple
Time used: 0.02 (sec). Leaf size: 32
dsolve(diff(diff(y(x),x),x) = -sin(x)/cos(x)*diff(y(x),x)-1/4*(2*x^2+x^2*sin(x)^2-24*cos(x)^2)/x^2/cos(x)^2*y(x)+cos(x)^(1/2),y(x), singsol=all)
\[ y \relax (x ) = \frac {\left (\sqrt {\cos }\relax (x )\right ) c_{2}}{x^{2}}+\left (\sqrt {\cos }\relax (x )\right ) x^{3} c_{1}-\frac {\left (\sqrt {\cos }\relax (x )\right ) x^{2}}{4} \]
✓ Solution by Mathematica
Time used: 0.11 (sec). Leaf size: 34
DSolve[y''[x] == Sqrt[Cos[x]] - (Sec[x]^2*(2*x^2 - 24*Cos[x]^2 + x^2*Sin[x]^2)*y[x])/(4*x^2) - Tan[x]*y'[x],y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {\left (x^4 (-5+4 c_2 x)+20 c_1\right ) \sqrt {\cos (x)}}{20 x^2} \\ \end{align*}