Internal problem ID [5909]
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: 37.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _linear, _nonhomogeneous]]
Solve \begin {gather*} \boxed {y^{\prime \prime }+y-\sqrt {2}\, \sin \left (\sqrt {2}\, t \right )=0} \end {gather*} With initial conditions \begin {align*} [y \relax (0) = 10, y^{\prime }\relax (0) = 0] \end {align*}
✓ Solution by Maple
Time used: 0.04 (sec). Leaf size: 24
dsolve([diff(y(t),t$2)+y(t)=sqrt(2)*sin(sqrt(2)*t),y(0) = 10, D(y)(0) = 0],y(t), singsol=all)
\[ y \relax (t ) = 2 \sin \relax (t )+10 \cos \relax (t )-\sqrt {2}\, \sin \left (t \sqrt {2}\right ) \]
✓ Solution by Mathematica
Time used: 0.095 (sec). Leaf size: 29
DSolve[{y''[t]+y[t]==Sqrt[2]*Sin[Sqrt[2]*t],{y[0]==10,y'[0]==0}},y[t],t,IncludeSingularSolutions -> True]
\begin{align*} y(t)\to 2 \sin (t)-\sqrt {2} \sin \left (\sqrt {2} t\right )+10 \cos (t) \\ \end{align*}