Internal problem ID [10841]
Book: Differential equations and the calculus of variations by L. ElSGOLTS. MIR PUBLISHERS,
MOSCOW, Third printing 1977.
Section: Chapter 2, DIFFERENTIAL EQUATIONS OF THE SECOND ORDER AND HIGHER.
Problems page 172
Problem number: Problem 35.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _linear, _nonhomogeneous]]
\[ \boxed {y^{\prime \prime }-2 y^{\prime }+2 y-x \,{\mathrm e}^{x} \cos \left (x \right )=0} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 36
dsolve(diff(y(x),x$2)-2*diff(y(x),x) +2*y(x)=x*exp(x)*cos(x),y(x), singsol=all)
\[ y \left (x \right ) = c_{2} \sin \left (x \right ) {\mathrm e}^{x}+{\mathrm e}^{x} \cos \left (x \right ) c_{1} +\frac {{\mathrm e}^{x} \left (x^{2} \sin \left (x \right )+\cos \left (x \right ) x -\sin \left (x \right )\right )}{4} \]
✓ Solution by Mathematica
Time used: 0.016 (sec). Leaf size: 37
DSolve[y''[x]-2*y'[x] +2*y[x]==x*Exp[x]*Cos[x],y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {1}{8} e^x \left (\left (2 x^2-1+8 c_1\right ) \sin (x)+2 (x+4 c_2) \cos (x)\right ) \\ \end{align*}