Internal problem ID [13870]
Book: Ordinary Differential Equations. An introduction to the fundamentals. Kenneth B. Howell.
second edition. CRC Press. FL, USA. 2020
Section: Chapter 28. The inverse Laplace transform. Additional Exercises. page 509
Problem number: 28.9 (a).
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _quadrature]]
\[ \boxed {y^{\prime \prime }={\mathrm e}^{t} \sin \left (t \right )} \] With initial conditions \begin {align*} [y \left (0\right ) = 0, y^{\prime }\left (0\right ) = 0] \end {align*}
✓ Solution by Maple
Time used: 4.703 (sec). Leaf size: 15
dsolve([diff(y(t),t$2)=exp(t)*sin(t),y(0) = 0, D(y)(0) = 0],y(t), singsol=all)
\[ y \left (t \right ) = -\frac {{\mathrm e}^{t} \cos \left (t \right )}{2}+\frac {t}{2}+\frac {1}{2} \]
✓ Solution by Mathematica
Time used: 0.056 (sec). Leaf size: 19
DSolve[{y''[t]==Exp[t]*Sin[t],{y[0]==0,y'[0]==0}},y[t],t,IncludeSingularSolutions -> True]
\[ y(t)\to \frac {1}{2} \left (t-e^t \cos (t)+1\right ) \]