Internal problem ID [13860]
Book: Ordinary Differential Equations. An introduction to the fundamentals. Kenneth B. Howell.
second edition. CRC Press. FL, USA. 2020
Section: Chapter 27. Differentiation and the Laplace transform. Additional Exercises. page
496
Problem number: 27.1 (L).
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _linear, _nonhomogeneous]]
\[ \boxed {y^{\prime \prime }+4 y^{\prime }+13 y=4 t +2 \,{\mathrm e}^{2 t} \sin \left (3 t \right )} \] With initial conditions \begin {align*} [y \left (0\right ) = 4, y^{\prime }\left (0\right ) = 3] \end {align*}
✓ Solution by Maple
Time used: 5.204 (sec). Leaf size: 47
dsolve([diff(y(t),t$2)+4*diff(y(t),t)+13*y(t)=4*t+2*exp(2*t)*sin(3*t),y(0) = 4, D(y)(0) = 3],y(t), singsol=all)
\[ y \left (t \right ) = -\frac {16}{169}+\frac {2 \cosh \left (2 t \right ) \left (346 \cos \left (3 t \right )+313 \sin \left (3 t \right )\right )}{169}+\frac {\left (-1423 \cos \left (3 t \right )-1226 \sin \left (3 t \right )\right ) \sinh \left (2 t \right )}{338}+\frac {4 t}{13} \]
✓ Solution by Mathematica
Time used: 1.331 (sec). Leaf size: 55
DSolve[{y''[t]+4*y'[t]+13*y[t]==4*t+2*Exp[2*t]*Sin[3*t],{y[0]==4,y'[0]==3}},y[t],t,IncludeSingularSolutions -> True]
\[ y(t)\to \frac {1}{676} e^{-2 t} \left (16 e^{2 t} (13 t-4)+\left (26 e^{4 t}+2478\right ) \sin (3 t)+\left (2807-39 e^{4 t}\right ) \cos (3 t)\right ) \]