Internal problem ID [4926]
Book: ADVANCED ENGINEERING MATHEMATICS. ERWIN KREYSZIG, HERBERT KREYSZIG,
EDWARD J. NORMINTON. 10th edition. John Wiley USA. 2011
Section: Chapter 6. Laplace Transforms. Problem set 6.2, page 216
Problem number: 1.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_linear, class A]]
Solve \begin {gather*} \boxed {y^{\prime }+\frac {26 y}{5}-\frac {97 \sin \left (2 t \right )}{5}=0} \end {gather*} With initial conditions \begin {align*} [y \relax (0) = 0] \end {align*}
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 23
dsolve([diff(y(t),t)+52/10*y(t)=194/10*sin(2*t),y(0) = 0],y(t), singsol=all)
\[ y \relax (t ) = -\frac {5 \cos \left (2 t \right )}{4}+\frac {13 \sin \left (2 t \right )}{4}+\frac {5 \,{\mathrm e}^{-\frac {26 t}{5}}}{4} \]
✓ Solution by Mathematica
Time used: 0.121 (sec). Leaf size: 31
DSolve[{y'[t]+52/10*y[t]==194/10*Sin[2*t],{y[0]==0}},y[t],t,IncludeSingularSolutions -> True]
\begin{align*} y(t)\to \frac {1}{4} \left (5 e^{-26 t/5}+13 \sin (2 t)-5 \cos (2 t)\right ) \\ \end{align*}