Internal problem ID [15307]
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. Trial and error method. Exercises page 132
Problem number: 537.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _linear, _nonhomogeneous]]
\[ \boxed {y^{\prime \prime }-3 y^{\prime }+2 y=x \,{\mathrm e}^{x}} \]
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 23
dsolve(diff(y(x),x$2)-3*diff(y(x),x)+2*y(x)=x*exp(x),y(x), singsol=all)
\[ y \left (x \right ) = -\frac {\left (-2 c_{1} {\mathrm e}^{x}+x^{2}-2 c_{2} +2 x \right ) {\mathrm e}^{x}}{2} \]
✓ Solution by Mathematica
Time used: 0.039 (sec). Leaf size: 33
DSolve[y''[x]-3*y'[x]+2*y[x]==x*Exp[x],y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \frac {1}{2} e^x \left (-x^2-2 x+2 \left (c_2 e^x-1+c_1\right )\right ) \]