Internal problem ID [12322]
Book: APPLIED DIFFERENTIAL EQUATIONS The Primary Course by Vladimir A.
Dobrushkin. CRC Press 2015
Section: Chapter 5.6 Laplace transform. Nonhomogeneous equations. Problems page
368
Problem number: Problem 2(l)[n].
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
\[ \boxed {3 y^{\prime \prime }+5 y^{\prime }-2 y=7 \,{\mathrm e}^{-2 t}} \] With initial conditions \begin {align*} [y \left (0\right ) = 3, y^{\prime }\left (0\right ) = 0] \end {align*}
✓ Solution by Maple
Time used: 4.922 (sec). Leaf size: 18
dsolve([3*diff(y(t),t$2)+5*diff(y(t),t)-2*y(t)=7*exp(-2*t),y(0) = 3, D(y)(0) = 0],y(t), singsol=all)
\[ y \left (t \right ) = -\left (-3 \,{\mathrm e}^{\frac {7 t}{3}}+t \right ) {\mathrm e}^{-2 t} \]
✓ Solution by Mathematica
Time used: 0.072 (sec). Leaf size: 23
DSolve[{3*y''[t]+5*y'[t]-2*y[t]==7*Exp[-2*t],{y[0]==3,y'[0]==0}},y[t],t,IncludeSingularSolutions -> True]
\[ y(t)\to 3 e^{t/3}-e^{-2 t} t \]