10.10.8 problem 8

Internal problem ID [1340]
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
Date solved : Monday, January 27, 2025 at 04:51:35 AM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

\begin{align*} y^{\prime \prime }+4 y&=3 \csc \left (2 t \right ) \end{align*}

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 35

dsolve(diff(y(t),t$2)+4*y(t) = 3*csc(2*t),y(t), singsol=all)
 

\[ y = -\frac {3 \ln \left (\csc \left (2 t \right )\right ) \sin \left (2 t \right )}{4}+\frac {\left (-6 t +4 c_1 \right ) \cos \left (2 t \right )}{4}+c_2 \sin \left (2 t \right ) \]

✓ Solution by Mathematica

Time used: 0.029 (sec). Leaf size: 39

DSolve[D[y[t],{t,2}]+4*y[t] ==3*Csc[2*t],y[t],t,IncludeSingularSolutions -> True]
 

\[ y(t)\to \left (-\frac {3 t}{2}+c_1\right ) \cos (2 t)+\frac {1}{4} \sin (2 t) (3 \log (\sin (2 t))+4 c_2) \]