76.17.13 problem 22

Internal problem ID [17628]
Book : Differential equations. An introduction to modern methods and applications. James Brannan, William E. Boyce. Third edition. Wiley 2015
Section : Chapter 4. Second order linear equations. Section 4.7 (Variation of parameters). Problems at page 280
Problem number : 22
Date solved : Monday, March 31, 2025 at 04:23:01 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

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

✓ Maple. Time used: 0.006 (sec). Leaf size: 15

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

\[ y = t \left ({\mathrm e}^{t} c_1 +c_2 -2 t \right ) \]

✓ Mathematica. Time used: 0.029 (sec). Leaf size: 20

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

\[ y(t)\to t \left (-2 t+c_2 e^t-2+c_1\right ) \]

✗ Sympy

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

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