Internal problem ID [10966]
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(f).
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
\[ \boxed {2 y^{\prime \prime }-3 y^{\prime }+17 y-17 t +1=0} \] With initial conditions \begin {align*} [y \left (0\right ) = -1, y^{\prime }\left (0\right ) = 2] \end {align*}
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 36
dsolve([2*diff(y(t),t$2)-3*diff(y(t),t)+17*y(t)=17*t-1,y(0) = -1, D(y)(0) = 2],y(t), singsol=all)
\[ y \left (t \right ) = \frac {125 \,{\mathrm e}^{\frac {3 t}{4}} \sin \left (\frac {\sqrt {127}\, t}{4}\right ) \sqrt {127}}{2159}-\frac {19 \,{\mathrm e}^{\frac {3 t}{4}} \cos \left (\frac {\sqrt {127}\, t}{4}\right )}{17}+t +\frac {2}{17} \]
✓ Solution by Mathematica
Time used: 0.006 (sec). Leaf size: 53
DSolve[{2*y''[t]-3*y'[t]+17*y[t]==17*t-1,{y[0]==-1,y'[0]==2}},y[t],t,IncludeSingularSolutions -> True]
\begin{align*} y(t)\to t+\frac {e^{3 t/4} \left (125 \sqrt {127} \sin \left (\frac {\sqrt {127} t}{4}\right )-2413 \cos \left (\frac {\sqrt {127} t}{4}\right )\right )}{2159}+\frac {2}{17} \\ \end{align*}