74.14.32 problem 32

Internal problem ID [16366]
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 : Monday, March 31, 2025 at 02:51:16 PM
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*}

✓ Maple. Time used: 0.002 (sec). Leaf size: 15

ode:=(t^2+t)*diff(diff(diff(y(t),t),t),t)+(-t^2+2)*diff(diff(y(t),t),t)-(t+2)*diff(y(t),t) = -2-t; 
dsolve(ode,y(t), singsol=all);
 

\[ y = c_2 \ln \left (t \right )+{\mathrm e}^{t} c_1 +t +c_3 \]

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

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

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

✗ Sympy

from sympy import * 
t = symbols("t") 
y = Function("y") 
ode = Eq(t + (2 - t**2)*Derivative(y(t), (t, 2)) - (t + 2)*Derivative(y(t), t) + (t**2 + t)*Derivative(y(t), (t, 3)) + 2,0) 
ics = {} 
dsolve(ode,func=y(t),ics=ics)
 

NotImplementedError : The given ODE Derivative(y(t), t) - (-t**2*Derivative(y(t), (t, 2)) + t**2*Derivative(y(t), (t, 3)) + t*Derivative(y(t), (t, 3)) + t + 2*Derivative(y(t), (t, 2)) + 2)/(t + 2) cannot be solved by the factorable group method