Internal problem ID [14565]
Book: INTRODUCTORY DIFFERENTIAL EQUATIONS. Martha L. Abell, James P. Braselton.
Fourth edition 2014. ElScAe. 2014
Section: Chapter 4. Higher Order Equations. Exercises 4.3, page 156
Problem number: 59.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _linear, _nonhomogeneous]]
\[ \boxed {y^{\prime \prime }+9 y=\left \{\begin {array}{cc} 2 t & 0\le t <\pi \\ 0 & \pi \le t \end {array}\right .} \] With initial conditions \begin {align*} [y \left (0\right ) = 0, y^{\prime }\left (0\right ) = 0] \end {align*}
✓ Solution by Maple
Time used: 0.719 (sec). Leaf size: 41
dsolve([diff(y(t),t$2)+9*y(t)=piecewise(0<=t and t<Pi,2*t,t>=Pi,0),y(0) = 0, D(y)(0) = 0],y(t), singsol=all)
\[ y \left (t \right ) = \frac {2 \left (\left \{\begin {array}{cc} 0 & t <0 \\ 3 t -\sin \left (3 t \right ) & t <\pi \\ -3 \cos \left (3 t \right ) \pi -2 \sin \left (3 t \right ) & \pi \le t \end {array}\right .\right )}{27} \]
✓ Solution by Mathematica
Time used: 0.038 (sec). Leaf size: 49
DSolve[{y''[t]+9*y[t]==Piecewise[{ {2*t,0<=t<Pi},{0,t>=Pi} }],{y[0]==0,y'[0]==0}},y[t],t,IncludeSingularSolutions -> True]
\[ y(t)\to \begin {array}{cc} \{ & \begin {array}{cc} 0 & t\leq 0 \\ -\frac {2}{27} (\sin (3 t)-3 t) & 0<t\leq \pi \\ -\frac {2}{27} (3 \pi \cos (3 t)+2 \sin (3 t)) & \text {True} \\ \end {array} \\ \end {array} \]