Internal problem ID [2862]
Book: Differential equations and linear algebra, Stephen W. Goode and Scott A Annin. Fourth
edition, 2015
Section: Chapter 10, The Laplace Transform and Some Elementary Applications. Exercises for
10.4. page 689
Problem number: Problem 24.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _linear, _nonhomogeneous]]
\[ \boxed {y^{\prime \prime }-3 y^{\prime }+2 y=3 \cos \left (t \right )+\sin \left (t \right )} \] With initial conditions \begin {align*} [y \left (0\right ) = 1, y^{\prime }\left (0\right ) = 1] \end {align*}
✓ Solution by Maple
Time used: 2.0 (sec). Leaf size: 23
dsolve([diff(y(t),t$2)-3*diff(y(t),t)+2*y(t)=3*cos(t)+sin(t),y(0) = 1, D(y)(0) = 1],y(t), singsol=all)
\[ y \left (t \right ) = \frac {7 \,{\mathrm e}^{2 t}}{5}-{\mathrm e}^{t}-\frac {4 \sin \left (t \right )}{5}+\frac {3 \cos \left (t \right )}{5} \]
✓ Solution by Mathematica
Time used: 0.112 (sec). Leaf size: 29
DSolve[{y''[t]-3*y'[t]+2*y[t]==3*Cos[t]+Sin[t],{y[0]==1,y'[0]==1}},y[t],t,IncludeSingularSolutions -> True]
\[ y(t)\to \frac {1}{5} \left (e^t \left (7 e^t-5\right )-4 \sin (t)+3 \cos (t)\right ) \]