74.14.33 problem 33

Internal problem ID [16438]
Book : INTRODUCTORY DIFFERENTIAL EQUATIONS. Martha L. Abell, James P. Braselton. Fourth edition 2014. ElScAe. 2014
Section : Chapter 4. Higher Order Equations. Exercises 4.6, page 187
Problem number : 33
Date solved : Tuesday, January 28, 2025 at 09:07:58 AM
CAS classification : [[_3rd_order, _with_linear_symmetries]]

\begin{align*} 2 t^{3} y^{\prime \prime \prime }+t^{2} y^{\prime \prime }+y^{\prime } t -y&=-3 t^{2} \end{align*}

With initial conditions

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

✓ Solution by Maple

Time used: 0.023 (sec). Leaf size: 14

dsolve([2*t^3*diff(y(t),t$3)+t^2*diff(y(t),t$2)+t*diff(y(t),t)-y(t)=-3*t^2,y(1) = 0, D(y)(1) = 1, (D@@2)(y)(1) = 0],y(t), singsol=all)
 

\[ y = -t \left (-2 \ln \left (t \right )+t -1\right ) \]

✓ Solution by Mathematica

Time used: 0.009 (sec). Leaf size: 16

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

\[ y(t)\to t (-t+2 \log (t)+1) \]