Internal problem ID [690]
Book: Elementary differential equations and boundary value problems, 10th ed., Boyce and
DiPrima
Section: Chapter 3, Second order linear equations, section 3.6, Variation of Parameters. page
190
Problem number: 8.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _linear, _nonhomogeneous]]
Solve \begin {gather*} \boxed {y^{\prime \prime }+4 y-3 \csc \left (2 t \right )=0} \end {gather*}
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 37
dsolve(diff(y(t),t$2)+4*y(t) = 3*csc(2*t),y(t), singsol=all)
\[ y \relax (t ) = c_{2} \sin \left (2 t \right )+\cos \left (2 t \right ) c_{1}-\frac {3 \ln \left (\frac {1}{\sin \left (2 t \right )}\right ) \sin \left (2 t \right )}{4}-\frac {3 \cos \left (2 t \right ) t}{2} \]
✓ Solution by Mathematica
Time used: 0.017 (sec). Leaf size: 39
DSolve[y''[t]+4*y[t] ==3*Csc[2*t],y[t],t,IncludeSingularSolutions -> True]
\begin{align*} y(t)\to \left (-\frac {3 t}{2}+c_1\right ) \cos (2 t)+\frac {1}{4} \sin (2 t) (3 \log (\sin (2 t))+4 c_2) \\ \end{align*}