Internal problem ID [8809]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 2, linear second order
Problem number: 1229.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _exact, _linear, _nonhomogeneous]]
Solve \begin {gather*} \boxed {\left (x^{2}+1\right ) y^{\prime \prime }+4 x y^{\prime }+2 y-2 \cos \relax (x )+2 x=0} \end {gather*}
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 41
dsolve((x^2+1)*diff(diff(y(x),x),x)+4*x*diff(y(x),x)+2*y(x)-2*cos(x)+2*x=0,y(x), singsol=all)
\[ y \relax (x ) = \frac {c_{1} x}{x^{2}+1}+\frac {c_{2}}{x^{2}+1}-\frac {x^{3}+6 \cos \relax (x )}{3 \left (x^{2}+1\right )} \]
✓ Solution by Mathematica
Time used: 0.026 (sec). Leaf size: 33
DSolve[2*x - 2*Cos[x] + 2*y[x] + 4*x*y'[x] + (1 + x^2)*y''[x] == 0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -\frac {x^3+6 \cos (x)-3 c_2 x-3 c_1}{3 x^2+3} \\ \end{align*}