Internal problem ID [4118]
Book: Ordinary Differential Equations, By Tenenbaum and Pollard. Dover, NY 1963
Section: Chapter 4. Higher order linear differential equations. Lesson 21. Undetermined
Coefficients
Problem number: Exercise 21.28, page 231.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
Solve \begin {gather*} \boxed {y^{\prime \prime }-5 y^{\prime }-6 y-{\mathrm e}^{3 x}=0} \end {gather*} With initial conditions \begin {align*} [y \relax (0) = 2, y^{\prime }\relax (0) = 1] \end {align*}
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 23
dsolve([diff(y(x),x$2)-5*diff(y(x),x)-6*y(x)=exp(3*x),y(0) = 2, D(y)(0) = 1],y(x), singsol=all)
\[ y \relax (x ) = \frac {45 \,{\mathrm e}^{-x}}{28}+\frac {10 \,{\mathrm e}^{6 x}}{21}-\frac {{\mathrm e}^{3 x}}{12} \]
✓ Solution by Mathematica
Time used: 0.021 (sec). Leaf size: 30
DSolve[{y''[x]-5*y'[x]-6*y[x]==Exp[3*x],{y[0]==2,y'[0]==1}},y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {1}{84} e^{-x} \left (-7 e^{4 x}+40 e^{7 x}+135\right ) \\ \end{align*}