Internal problem ID [5910]
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. 7.2.2 TRANSFORMS OF DERIVATIVES
Page 289
Problem number: 38.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
Solve \begin {gather*} \boxed {y^{\prime \prime }+9 y-{\mathrm e}^{t}=0} \end {gather*} With initial conditions \begin {align*} [y \relax (0) = 0, y^{\prime }\relax (0) = 0] \end {align*}
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 21
dsolve([diff(y(t),t$2)+9*y(t)=exp(t),y(0) = 0, D(y)(0) = 0],y(t), singsol=all)
\[ y \relax (t ) = -\frac {\sin \left (3 t \right )}{30}-\frac {\cos \left (3 t \right )}{10}+\frac {{\mathrm e}^{t}}{10} \]
✓ Solution by Mathematica
Time used: 0.076 (sec). Leaf size: 27
DSolve[{y''[t]+9*y[t]==Exp[t],{y[0]==0,y'[0]==0}},y[t],t,IncludeSingularSolutions -> True]
\begin{align*} y(t)\to \frac {1}{30} \left (3 e^t-\sin (3 t)-3 \cos (3 t)\right ) \\ \end{align*}