74.14.32 problem 32

Internal problem ID [16437]
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 : 32
Date solved : Tuesday, January 28, 2025 at 09:07:57 AM
CAS classification : [[_3rd_order, _missing_y]]

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

✓ Solution by Maple

Time used: 0.005 (sec). Leaf size: 15

dsolve((t^2+t)*diff(y(t),t$3)+(2-t^2)*diff(y(t),t$2)-(t+2)*diff(y(t),t)=-2-t,y(t), singsol=all)
 

\[ y = c_{2} \ln \left (t \right )+c_{1} {\mathrm e}^{t}+t +c_{3} \]

✓ Solution by Mathematica

Time used: 4.699 (sec). Leaf size: 303

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

\[ y(t)\to \int _1^t\exp \left (\int _1^{K[6]}-\frac {K[1]+2}{2 K[1]+2}dK[1]-\frac {1}{2} \int _1^{K[6]}\frac {2-K[2]^2}{K[2]^2+K[2]}dK[2]\right ) \left (c_1+\int _1^{K[6]}\exp \left (-2 \int _1^{K[3]}-\frac {K[1]+2}{2 K[1]+2}dK[1]\right )dK[3] \left (c_2+\int _1^{K[6]}-\frac {\exp \left (\int _1^{K[5]}-\frac {K[1]+2}{2 K[1]+2}dK[1]+\frac {1}{2} \int _1^{K[5]}\frac {2-K[2]^2}{K[2]^2+K[2]}dK[2]\right ) (K[5]+2)}{K[5] (K[5]+1)}dK[5]\right )+\int _1^{K[6]}\frac {\exp \left (\int _1^{K[4]}-\frac {K[1]+2}{2 K[1]+2}dK[1]+\frac {1}{2} \int _1^{K[4]}\frac {2-K[2]^2}{K[2]^2+K[2]}dK[2]\right ) (K[4]+2) \int _1^{K[4]}\exp \left (-2 \int _1^{K[3]}-\frac {K[1]+2}{2 K[1]+2}dK[1]\right )dK[3]}{K[4] (K[4]+1)}dK[4]\right )dK[6]+c_3 \]