Internal problem ID [14708]
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.
ODE order: 3.
ODE degree: 1.
CAS Maple gives this as type [[_3rd_order, _with_linear_symmetries]]
\[ \boxed {2 t^{3} y^{\prime \prime \prime }+t^{2} y^{\prime \prime }+y^{\prime } t -y=-3 t^{2}} \] 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: 0.031 (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)
\[ y \left (t \right ) = -t \left (-2 \ln \left (t \right )+t -1\right ) \]
✓ Solution by Mathematica
Time used: 0.008 (sec). Leaf size: 16
DSolve[{2*t^3*y'''[t]+t^2*y''[t]+t*y'[t]-y[t]==-3*t^2,{y[1]==0,y'[1]==1,y''[1]==0}},y[t],t,IncludeSingularSolutions -> True]
\[ y(t)\to t (-t+2 \log (t)+1) \]