Internal problem ID [12000]
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(k)[l].
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _linear, _nonhomogeneous]]
\[ \boxed {2 y^{\prime \prime }+y^{\prime }-y=4 \sin \left (t \right )} \] With initial conditions \begin {align*} [y \left (0\right ) = 0, y^{\prime }\left (0\right ) = -4] \end {align*}
✓ Solution by Maple
Time used: 0.032 (sec). Leaf size: 25
dsolve([2*diff(y(t),t$2)+diff(y(t),t)-y(t)=4*sin(t),y(0) = 0, D(y)(0) = -4],y(t), singsol=all)
\[ y \left (t \right ) = -\frac {2 \,{\mathrm e}^{-t} \left (4 \,{\mathrm e}^{\frac {3 t}{2}}-5+\left (\cos \left (t \right )+3 \sin \left (t \right )\right ) {\mathrm e}^{t}\right )}{5} \]
✓ Solution by Mathematica
Time used: 0.037 (sec). Leaf size: 34
DSolve[{2*y''[t]+y'[t]-y[t]==4*Sin[t],{y[0]==0,y'[0]==-4}},y[t],t,IncludeSingularSolutions -> True]
\[ y(t)\to \frac {2}{5} \left (5 e^{-t}-4 e^{t/2}-3 \sin (t)-\cos (t)\right ) \]