Internal problem ID [14629]
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 (a).
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
\[ \boxed {t^{2} y^{\prime \prime }-4 y^{\prime } t +\left (t^{2}+6\right ) y=t^{3}+2 t} \] With initial conditions \begin {align*} [y \left (0\right ) = 0, y^{\prime }\left (0\right ) = 1] \end {align*}
✓ Solution by Maple
Time used: 0.031 (sec). Leaf size: 18
dsolve([t^2*diff(y(t),t$2)-4*t*diff(y(t),t)+(t^2+6)*y(t)=t^3+2*t,y(0) = 0, D(y)(0) = 1],y(t), singsol=all)
\[ y \left (t \right ) = t \left (\sin \left (t \right ) t c_{2} +t \cos \left (t \right ) c_{1} +1\right ) \]
✓ Solution by Mathematica
Time used: 0.22 (sec). Leaf size: 37
DSolve[{t^2*y''[t]-4*t*y'[t]+(t^2+6)*y[t]==t^3+2*t,{y[0]==0,y'[0]==1}},y[t],t,IncludeSingularSolutions -> True]
\[ y(t)\to t+t^2 \left (c_1 e^{-i t}-\frac {1}{2} i c_2 e^{i t}\right ) \]