Internal problem ID [15370]
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: 601.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
\[ \boxed {y^{\prime \prime }-6 y^{\prime }+9 y=16 \,{\mathrm e}^{-x}+9 x -6} \] With initial conditions \begin {align*} [y \left (0\right ) = 1, y^{\prime }\left (0\right ) = 1] \end {align*}
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 16
dsolve([diff(y(x),x$2)-6*diff(y(x),x)+9*y(x)=16*exp(-x)+9*x-6,y(0) = 1, D(y)(0) = 1],y(x), singsol=all)
\[ y \left (x \right ) = {\mathrm e}^{3 x} x +x +{\mathrm e}^{-x} \]
✓ Solution by Mathematica
Time used: 0.28 (sec). Leaf size: 19
DSolve[{y''[x]-6*y'[x]+9*y[x]==16*Exp[-x]+9*x-6,{y[0]==1,y'[0]==1}},y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to e^{3 x} x+x+e^{-x} \]