Internal problem ID [9767]
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]]
\[ \boxed {y^{\prime \prime }+\frac {\sin \left (x \right ) y^{\prime }}{\cos \left (x \right )}+\frac {\left (2 x^{2}+x^{2} \sin \left (x \right )^{2}-24 \cos \left (x \right )^{2}\right ) y}{4 x^{2} \cos \left (x \right )^{2}}=\sqrt {\cos \left (x \right )}} \]
✓ Solution by Maple
Time used: 0.016 (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)
\[ y \left (x \right ) = \frac {\sqrt {\cos \left (x \right )}\, c_{2}}{x^{2}}+\sqrt {\cos \left (x \right )}\, x^{3} c_{1} -\frac {\sqrt {\cos \left (x \right )}\, x^{2}}{4} \]
✓ Solution by Mathematica
Time used: 0.22 (sec). Leaf size: 35
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]
\[ y(x)\to \frac {\left (4 c_2 x^5-5 x^4+20 c_1\right ) \sqrt {\cos (x)}}{20 x^2} \]