74.12.53 problem 61 (a)

Internal problem ID [16360]
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)
Date solved : Tuesday, January 28, 2025 at 09:06:52 AM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} t^{2} y^{\prime \prime }-4 y^{\prime } t +\left (t^{2}+6\right ) y&=t^{3}+2 t \end{align*}

With initial conditions

\begin{align*} y \left (0\right )&=0\\ y^{\prime }\left (0\right )&=1 \end{align*}

✓ Solution by Maple

Time used: 0.102 (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)
 

\[ y = t \left (\sin \left (t \right ) t c_{2} +\cos \left (t \right ) t c_{1} +1\right ) \]

✓ Solution by Mathematica

Time used: 0.329 (sec). Leaf size: 37

DSolve[{t^2*D[y[t],{t,2}]-4*t*D[y[t],t]+(t^2+6)*y[t]==t^3+2*t,{y[0]==0,Derivative[1][y][0] ==1}},y[t],t,IncludeSingularSolutions -> True]
 

\[ y(t)\to t+t^2 \left (c_1 e^{-i t}-\frac {1}{2} i c_2 e^{i t}\right ) \]