Internal problem ID [14470]
Book: INTRODUCTORY DIFFERENTIAL EQUATIONS. Martha L. Abell, James P. Braselton.
Fourth edition 2014. ElScAe. 2014
Section: Chapter 4. Higher Order Equations. Exercises 4.1, page 141
Problem number: 44.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
\[ \boxed {4 t^{2} y^{\prime \prime }+4 y^{\prime } t +\left (36 t^{2}-1\right ) y=0} \] Given that one solution of the ode is \begin {align*} y_1 &= \frac {1}{\sqrt {t}} \end {align*}
✓ Solution by Maple
Time used: 0.063 (sec). Leaf size: 21
dsolve([4*t^2*diff(y(t),t$2)+4*t*diff(y(t),t)+(36*t^2-1)*y(t)=0,1/t^(1/2)],singsol=all)
\[ y \left (t \right ) = \frac {c_{1} \sin \left (3 t \right )+\cos \left (3 t \right ) c_{2}}{\sqrt {t}} \]
✓ Solution by Mathematica
Time used: 0.045 (sec). Leaf size: 39
DSolve[4*t^2*y''[t]+4*t*y'[t]+(36*t^2-1)*y[t]==0,y[t],t,IncludeSingularSolutions -> True]
\[ y(t)\to \frac {e^{-3 i t} \left (6 c_1-i c_2 e^{6 i t}\right )}{6 \sqrt {t}} \]