Internal problem ID [14864]
Book: INTRODUCTORY DIFFERENTIAL EQUATIONS. Martha L. Abell, James P. Braselton.
Fourth edition 2014. ElScAe. 2014
Section: Chapter 4. Higher Order Equations. Chapter 4 review exercises, page 219
Problem number: 43.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
\[ \boxed {y^{\prime \prime }+3 y^{\prime }-4 y={\mathrm e}^{t}} \] With initial conditions \begin {align*} [y \left (0\right ) = 0, y^{\prime }\left (0\right ) = 4] \end {align*}
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 20
dsolve([diff(y(t),t$2)+3*diff(y(t),t)-4*y(t)=exp(t),y(0) = 0, D(y)(0) = 4],y(t), singsol=all)
\[ y \left (t \right ) = \frac {\left (5 t +19\right ) {\mathrm e}^{-4 t} {\mathrm e}^{5 t}}{25}-\frac {19 \,{\mathrm e}^{-4 t}}{25} \]
✓ Solution by Mathematica
Time used: 0.031 (sec). Leaf size: 27
DSolve[{y''[t]+3*y'[t]-4*y[t]==Exp[t],{y[0]==0,y'[0]==4}},y[t],t,IncludeSingularSolutions -> True]
\[ y(t)\to \frac {1}{25} e^{-4 t} \left (e^{5 t} (5 t+19)-19\right ) \]