Internal problem ID [14620]
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: 45.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _linear, _nonhomogeneous]]
\[ \boxed {y^{\prime \prime }+9 y=\csc \left (3 t \right )} \] With initial conditions \begin {align*} \left [y \left (\frac {\pi }{12}\right ) = 0, y^{\prime }\left (\frac {\pi }{12}\right ) = 1\right ] \end {align*}
✓ Solution by Maple
Time used: 0.125 (sec). Leaf size: 46
dsolve([diff(y(t),t$2)+9*y(t)=csc(3*t),y(1/12*Pi) = 0, D(y)(1/12*Pi) = 1],y(t), singsol=all)
\[ y \left (t \right ) = -\frac {\ln \left (\csc \left (3 t \right )\right ) \sin \left (3 t \right )}{9}+\frac {\left (-12 t +\pi -6 \sqrt {2}\right ) \cos \left (3 t \right )}{36}+\frac {\sin \left (3 t \right ) \left (3 \sqrt {2}+\ln \left (2\right )\right )}{18} \]
✓ Solution by Mathematica
Time used: 0.03 (sec). Leaf size: 51
DSolve[{y''[t]+9*y[t]==Csc[3*t],{y[Pi/12]==0,y'[Pi/12]==1}},y[t],t,IncludeSingularSolutions -> True]
\[ y(t)\to \frac {1}{36} \left (\left (\pi -6 \left (2 t+\sqrt {2}\right )\right ) \cos (3 t)+2 \sin (3 t) \left (2 \log (\sin (3 t))+3 \sqrt {2}+\log (2)\right )\right ) \]