Internal problem ID [14634]
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: 63 (c).
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _linear, _nonhomogeneous]]
\[ \boxed {4 t^{2} y^{\prime \prime }+4 y^{\prime } t +\left (16 t^{2}-1\right ) y=16 t^{\frac {3}{2}}} \] With initial conditions \begin {align*} [y \left (\pi \right ) = 0, y^{\prime }\left (2 \pi \right ) = 0] \end {align*}
✓ Solution by Maple
Time used: 0.094 (sec). Leaf size: 15
dsolve([4*t^2*diff(y(t),t$2)+4*t*diff(y(t),t)+(16*t^2-1)*y(t)=16*t^(3/2),y(Pi) = 0, D(y)(2*Pi) = 0],y(t), singsol=all)
\[ y \left (t \right ) = -\frac {-1+\cos \left (2 t \right )}{\sqrt {t}} \]
✓ Solution by Mathematica
Time used: 0.06 (sec). Leaf size: 32
DSolve[{4*t^2*y''[t]+4*t*y'[t]+(16*t^2-1)*y[t]==16*t^(3/2),{y[Pi]==0,y'[2*Pi]==0}},y[t],t,IncludeSingularSolutions -> True]
\[ y(t)\to -\frac {e^{-2 i t} \left (-1+e^{2 i t}\right )^2}{2 \sqrt {t}} \]