Internal problem ID [12905]
Book: DIFFERENTIAL EQUATIONS by Paul Blanchard, Robert L. Devaney, Glen R. Hall. 4th
edition. Brooks/Cole. Boston, USA. 2012
Section: Chapter 6. Laplace transform. Section 6.3 page 600
Problem number: 29.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
\[ \boxed {y^{\prime \prime }-4 y^{\prime }+5 y=2 \,{\mathrm e}^{t}} \] With initial conditions \begin {align*} [y \left (0\right ) = 3, y^{\prime }\left (0\right ) = 1] \end {align*}
✓ Solution by Maple
Time used: 0.078 (sec). Leaf size: 20
dsolve([diff(y(t),t$2)-4*diff(y(t),t)+5*y(t)=2*exp(t),y(0) = 3, D(y)(0) = 1],y(t), singsol=all)
\[ y = \left (2 \cos \left (t \right )-4 \sin \left (t \right )\right ) {\mathrm e}^{2 t}+{\mathrm e}^{t} \]
✓ Solution by Mathematica
Time used: 0.029 (sec). Leaf size: 25
DSolve[{y''[t]-4*y'[t]+5*y[t]==2*Exp[t],{y[0]==3,y'[0]==1}},y[t],t,IncludeSingularSolutions -> True]
\[ y(t)\to e^t \left (-4 e^t \sin (t)+2 e^t \cos (t)+1\right ) \]