Internal problem ID [14615]
Book: INTRODUCTORY DIFFERENTIAL EQUATIONS. Martha L. Abell, James P. Braselton.
Fourth edition 2014. ElScAe. 2014
Section: Chapter 4. Higher Order Equations. Exercises 4.4, page 163
Problem number: 40.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _linear, _nonhomogeneous]]
\[ \boxed {y^{\prime \prime }+9 y=\frac {\csc \left (3 t \right )}{2}} \] With initial conditions \begin {align*} \left [y \left (\frac {\pi }{4}\right ) = \sqrt {2}, y^{\prime }\left (\frac {\pi }{4}\right ) = 0\right ] \end {align*}
✓ Solution by Maple
Time used: 0.11 (sec). Leaf size: 38
dsolve([diff(y(t),t$2)+9*y(t)=1/2*csc(3*t),y(1/4*Pi) = 2^(1/2), D(y)(1/4*Pi) = 0],y(t), singsol=all)
\[ y \left (t \right ) = -\frac {\ln \left (\csc \left (3 t \right )\right ) \sin \left (3 t \right )}{18}+\frac {\left (-24-4 t +\pi \right ) \cos \left (3 t \right )}{24}+\frac {\left (\ln \left (2\right )+36\right ) \sin \left (3 t \right )}{36} \]
✓ Solution by Mathematica
Time used: 0.036 (sec). Leaf size: 40
DSolve[{y''[t]+9*y[t]==1/2*Csc[3*t],{y[Pi/4]==Sqrt[2],y'[Pi/4]==0}},y[t],t,IncludeSingularSolutions -> True]
\[ y(t)\to \frac {1}{72} (3 (\pi -4 (t+6)) \cos (3 t)+2 \sin (3 t) (2 \log (\sin (3 t))+36+\log (2))) \]