Internal problem ID [8671]
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]]
Solve \begin {gather*} \boxed {x \left (y^{\prime \prime }+y\right )-\cos \relax (x )=0} \end {gather*}
✓ Solution by Maple
Time used: 0.001 (sec). Leaf size: 35
dsolve(x*(diff(diff(y(x),x),x)+y(x))-cos(x)=0,y(x), singsol=all)
\[ y \relax (x ) = \sin \relax (x ) c_{2}+\cos \relax (x ) c_{1}+\frac {\sin \relax (x ) \ln \relax (x )}{2}+\frac {\sin \relax (x ) \cosineIntegral \left (2 x \right )}{2}-\frac {\sinIntegral \left (2 x \right ) \cos \relax (x )}{2} \]
✓ Solution by Mathematica
Time used: 0.014 (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) (\text {CosIntegral}(2 x)+\log (x)+2 c_2)+\cos (x) (-\text {Si}(2 x)+2 c_1)) \\ \end{align*}