Internal problem ID [6557]
Book: Own collection of miscellaneous problems
Section: section 5.0
Problem number: 17.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
Solve \begin {gather*} \boxed {y^{\prime \prime }+3 y^{\prime }-4 y-6 \,{\mathrm e}^{2 t -2}=0} \end {gather*} With initial conditions \begin {align*} [y \relax (1) = 4, y^{\prime }\relax (1) = 5] \end {align*}
✓ Solution by Maple
Time used: 0.031 (sec). Leaf size: 17
dsolve([diff(y(t),t$2)+3*diff(y(t),t)-4*y(t)=6*exp(2*t-2),y(1) = 4, D(y)(1) = 5],y(t), singsol=all)
\[ y \relax (t ) = 3 \,{\mathrm e}^{t -1}+{\mathrm e}^{2 t -2} \]
✓ Solution by Mathematica
Time used: 0.047 (sec). Leaf size: 18
DSolve[{y''[t]+3*y'[t]-4*y[t]==6*Exp[2*t-2],{y[1]==4,y'[1]==5}},y[t],t,IncludeSingularSolutions -> True]
\begin{align*} y(t)\to e^{t-2} \left (e^t+3 e\right ) \\ \end{align*}