Internal problem ID [6691]
Book: DIFFERENTIAL EQUATIONS with Boundary Value Problems. DENNIS G. ZILL,
WARREN S. WRIGHT, MICHAEL R. CULLEN. Brooks/Cole. Boston, MA. 2013. 8th
edition.
Section: CHAPTER 7 THE LAPLACE TRANSFORM. 7.4.1 DERIVATIVES OF A
TRANSFORM. Page 309
Problem number: 12.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _linear, _nonhomogeneous]]
\[ \boxed {y^{\prime \prime }+y=\sin \left (t \right )} \] With initial conditions \begin {align*} [y \left (0\right ) = 1, y^{\prime }\left (0\right ) = -1] \end {align*}
✓ Solution by Maple
Time used: 1.735 (sec). Leaf size: 16
dsolve([diff(y(t),t$2)+y(t)=sin(t),y(0) = 1, D(y)(0) = -1],y(t), singsol=all)
\[ y \left (t \right ) = -\frac {\sin \left (t \right )}{2}-\frac {\cos \left (t \right ) \left (t -2\right )}{2} \]
✓ Solution by Mathematica
Time used: 0.03 (sec). Leaf size: 21
DSolve[{y''[t]+y[t]==Sin[t],{y[0]==1,y'[0]==-1}},y[t],t,IncludeSingularSolutions -> True]
\[ y(t)\to -\frac {\sin (t)}{2}-\frac {1}{2} t \cos (t)+\cos (t) \]