Internal problem ID [9426]
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]]
\[ \boxed {x \left (y^{\prime \prime }+y\right )=\cos \left (x \right )} \]
✓ 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: 0.041 (sec). Leaf size: 41
DSolve[-Cos[x] + x*(y[x] + y''[x]) == 0,y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \frac {1}{2} (\operatorname {CosIntegral}(2 x) \sin (x)-\text {Si}(2 x) \cos (x)+\log (x) \sin (x))+c_1 \cos (x)+c_2 \sin (x) \]