Internal problem ID [15340]
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: 571.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _linear, _nonhomogeneous]]
\[ \boxed {y^{\prime \prime }-2 y^{\prime }-3 y=2 x +{\mathrm e}^{-x}-2 \,{\mathrm e}^{3 x}} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 37
dsolve(diff(y(x),x$2)-2*diff(y(x),x)-3*y(x)=2*x+exp(-x)-2*exp(3*x),y(x), singsol=all)
\[ y \left (x \right ) = \frac {4}{9}+\frac {\left (-1-4 x +16 c_{1} \right ) {\mathrm e}^{-x}}{16}+\frac {\left (1-4 x +8 c_{2} \right ) {\mathrm e}^{3 x}}{8}-\frac {2 x}{3} \]
✓ Solution by Mathematica
Time used: 0.501 (sec). Leaf size: 51
DSolve[y''[x]-2*y'[x]-3*y[x]==2*x+Exp[-x]-2*Exp[3*x],y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \frac {1}{144} e^{-x} \left (e^x (64-96 x)-9 (4 x+1-16 c_1)-18 e^{4 x} (4 x-1-8 c_2)\right ) \]