Internal problem ID [15363]
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. Initial value problem. Exercises page 140
Problem number: 594.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _linear, _nonhomogeneous]]
\[ \boxed {y^{\prime \prime }-5 y^{\prime }+6 y=\left (12 x -7\right ) {\mathrm e}^{-x}} \] With initial conditions \begin {align*} [y \left (0\right ) = 0, y^{\prime }\left (0\right ) = 0] \end {align*}
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 21
dsolve([diff(y(x),x$2)-5*diff(y(x),x)+6*y(x)=(12*x-7)*exp(-x),y(0) = 0, D(y)(0) = 0],y(x), singsol=all)
\[ y \left (x \right ) = {\mathrm e}^{2 x}-{\mathrm e}^{3 x}+{\mathrm e}^{-x} x \]
✓ Solution by Mathematica
Time used: 0.021 (sec). Leaf size: 25
DSolve[{y''[x]-5*y'[x]+6*y[x]==(12*x-7)*Exp[-x],{y[0]==0,y'[0]==0}},y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to e^{-x} \left (x+e^{3 x}-e^{4 x}\right ) \]