Internal problem ID [14628]
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: 61.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
\[ \boxed {t^{2} y^{\prime \prime }-4 y^{\prime } t +\left (t^{2}+6\right ) y=0} \] Given that one solution of the ode is \begin {align*} y_1 &= \cos \left (t \right ) t^{2} \end {align*}
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 17
dsolve([t^2*diff(y(t),t$2)-4*t*diff(y(t),t)+(t^2+6)*y(t)=0,t^2*cos(t)],singsol=all)
\[ y \left (t \right ) = t^{2} \left (c_{1} \sin \left (t \right )+c_{2} \cos \left (t \right )\right ) \]
✓ Solution by Mathematica
Time used: 0.053 (sec). Leaf size: 37
DSolve[t^2*y''[t]-4*t*y'[t]+(t^2+6)*y[t]==0,y[t],t,IncludeSingularSolutions -> True]
\[ y(t)\to \frac {1}{2} e^{-i t} t^2 \left (2 c_1-i c_2 e^{2 i t}\right ) \]