Internal problem ID [15330]
Book: A book of problems in ordinary differential equations. M.L. KRASNOV, A.L. KISELYOV,
G.I. MARKARENKO. MIR, MOSCOW. 1983
Section: Chapter 2 (Higher order ODE’s). Section 15.3 Nonhomogeneous linear equations with
constant coefficients. Superposition principle. Exercises page 137
Problem number: 561.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _linear, _nonhomogeneous]]
\[ \boxed {y^{\prime \prime }-2 y^{\prime }+y=2+{\mathrm e}^{x} \sin \left (x \right )} \]
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 18
dsolve(diff(y(x),x$2)-2*diff(y(x),x)+y(x)=2+exp(x)*sin(x),y(x), singsol=all)
\[ y \left (x \right ) = 2+\left (c_{1} x +c_{2} -\sin \left (x \right )\right ) {\mathrm e}^{x} \]
✓ Solution by Mathematica
Time used: 0.145 (sec). Leaf size: 25
DSolve[y''[x]-2*y'[x]+y[x]==2+Exp[x]*Sin[x],y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to -e^x \sin (x)+e^x (c_2 x+c_1)+2 \]