Internal problem ID [8669]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 2, linear second order
Problem number: 1091.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _linear, _nonhomogeneous]]
\[ \boxed {x \left (y^{\prime \prime }+y\right )-\cos \left (x \right )=0} \]
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 35
dsolve(x*(diff(diff(y(x),x),x)+y(x))-cos(x)=0,y(x), singsol=all)
\[ y \left (x \right ) = \sin \left (x \right ) c_{2} +c_{1} \cos \left (x \right )+\frac {\sin \left (x \right ) \ln \left (x \right )}{2}+\frac {\sin \left (x \right ) \operatorname {Ci}\left (2 x \right )}{2}-\frac {\operatorname {Si}\left (2 x \right ) \cos \left (x \right )}{2} \]
✓ Solution by Mathematica
Time used: 0.015 (sec). Leaf size: 38
DSolve[-Cos[x] + x*(y[x] + y''[x]) == 0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {1}{2} (\sin (x) (\operatorname {CosIntegral}(2 x)+\log (x)+2 c_2)+\cos (x) (-\text {Si}(2 x)+2 c_1)) \\ \end{align*}