Internal problem ID [5924]
Book: DIFFERENTIAL EQUATIONS with Boundary Value Problems. DENNIS G. ZILL,
WARREN S. WRIGHT, MICHAEL R. CULLEN. Brooks/Cole. Boston, MA. 2013. 8th
edition.
Section: CHAPTER 7 THE LAPLACE TRANSFORM. 7.3.1 TRANSLATION ON THE s-AXIS. Page
297
Problem number: 30.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
Solve \begin {gather*} \boxed {y^{\prime \prime }-2 y^{\prime }+5 y-t -1=0} \end {gather*} With initial conditions \begin {align*} [y \relax (0) = 0, y^{\prime }\relax (0) = 4] \end {align*}
✓ Solution by Maple
Time used: 0.01 (sec). Leaf size: 25
dsolve([diff(y(t),t$2)-2*diff(y(t),t)+5*y(t)=1+t,y(0) = 0, D(y)(0) = 4],y(t), singsol=all)
\[ y \relax (t ) = \frac {51 \,{\mathrm e}^{t} \sin \left (2 t \right )}{25}-\frac {7 \,{\mathrm e}^{t} \cos \left (2 t \right )}{25}+\frac {t}{5}+\frac {7}{25} \]
✓ Solution by Mathematica
Time used: 0.004 (sec). Leaf size: 31
DSolve[{y''[t]-2*y'[t]+5*y[t]==1+t,{y[0]==0,y'[0]==4}},y[t],t,IncludeSingularSolutions -> True]
\begin{align*} y(t)\to \frac {1}{25} \left (5 t+e^t (51 \sin (2 t)-7 \cos (2 t))+7\right ) \\ \end{align*}