56.5.17 problem 17

Internal problem ID [8978]
Book : Own collection of miscellaneous problems
Section : section 5.0
Problem number : 17
Date solved : Monday, January 27, 2025 at 05:26:07 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} y^{\prime \prime }+3 y^{\prime }-4 y&=6 \,{\mathrm e}^{2 t -2} \end{align*}

Using Laplace method With initial conditions

\begin{align*} y \left (1\right )&=4\\ y^{\prime }\left (1\right )&=5 \end{align*}

✓ Solution by Maple

Time used: 1.192 (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)
 

\[ y = 3 \,{\mathrm e}^{t -1}+{\mathrm e}^{2 t -2} \]

✓ Solution by Mathematica

Time used: 0.076 (sec). Leaf size: 18

DSolve[{D[y[t],{t,2}]+3*D[y[t],t]-4*y[t]==6*Exp[2*t-2],{y[1]==4,Derivative[1][y][1]==5}},y[t],t,IncludeSingularSolutions -> True]
 

\[ y(t)\to e^{t-2} \left (e^t+3 e\right ) \]