Internal problem ID [11996]
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(h).
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
\[ \boxed {y^{\prime \prime }-2 y^{\prime }+5 y=t +2} \] With initial conditions \begin {align*} [y \left (0\right ) = 4, y^{\prime }\left (0\right ) = 1] \end {align*}
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 25
dsolve([diff(y(t),t$2)-2*diff(y(t),t)+5*y(t)=2+t,y(0) = 4, D(y)(0) = 1],y(t), singsol=all)
\[ y \left (t \right ) = -\frac {34 \,{\mathrm e}^{t} \sin \left (2 t \right )}{25}+\frac {88 \,{\mathrm e}^{t} \cos \left (2 t \right )}{25}+\frac {t}{5}+\frac {12}{25} \]
✓ Solution by Mathematica
Time used: 0.029 (sec). Leaf size: 32
DSolve[{y''[t]-2*y'[t]+5*y[t]==2+t,{y[0]==4,y'[0]==1}},y[t],t,IncludeSingularSolutions -> True]
\[ y(t)\to \frac {1}{25} \left (5 t-34 e^t \sin (2 t)+88 e^t \cos (2 t)+12\right ) \]