Internal problem ID [15323]
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: 554.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _linear, _nonhomogeneous]]
\[ \boxed {y^{\prime \prime }-2 y^{\prime }+2 y=\left (1+\sin \left (x \right )\right ) {\mathrm e}^{x}} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 26
dsolve(diff(y(x),x$2)-2*diff(y(x),x)+2*y(x)=(1+sin(x))*exp(x),y(x), singsol=all)
\[ y \left (x \right ) = -\frac {{\mathrm e}^{x} \left (\left (x -2 c_{1} \right ) \cos \left (x \right )-2+\left (-2 c_{2} -1\right ) \sin \left (x \right )\right )}{2} \]
✓ Solution by Mathematica
Time used: 0.194 (sec). Leaf size: 32
DSolve[y''[x]-2*y'[x]+2*y[x]==(1+Sin[x])*Exp[x],y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \frac {1}{2} e^x (-((x-2 c_2) \cos (x))+2 (1+c_1) \sin (x)+2) \]