80.1.10 problem 10

Internal problem ID [21128]
Book : A Textbook on Ordinary Differential Equations by Shair Ahmad and Antonio Ambrosetti. Second edition. ISBN 978-3-319-16407-6. Springer 2015
Section : Chapter 1. First order linear differential equations. Excercise 1.5 at page 13
Problem number : 10
Date solved : Thursday, October 02, 2025 at 07:09:33 PM
CAS classification : [_linear]

\begin{align*} t^{2} x^{\prime }-2 x t&=t^{5} \end{align*}

With initial conditions

\begin{align*} x \left (0\right )&=0 \\ \end{align*}

✓ Maple. Time used: 0.014 (sec). Leaf size: 16

ode:=t^2*diff(x(t),t)-2*t*x(t) = t^5; 
ic:=[x(0) = 0]; 
dsolve([ode,op(ic)],x(t), singsol=all);
 

\[ x = \frac {\left (t^{2}+2 c_1 \right ) t^{2}}{2} \]

✓ Mathematica. Time used: 0.074 (sec). Leaf size: 19

ode=t^2*D[x[t],t]-2*t*x[t]==t^5; 
ic={x[0]==0}; 
DSolve[{ode,ic},x[t],t,IncludeSingularSolutions->True]
 

\begin{align*} x(t)&\to \frac {t^4}{2}+c_1 t^2 \end{align*}

✗ Sympy

from sympy import * 
t = symbols("t") 
x = Function("x") 
ode = Eq(-t**5 + t**2*Derivative(x(t), t) - 2*t*x(t),0) 
ics = {x(0): 0} 
dsolve(ode,func=x(t),ics=ics)
 

ValueError : Couldnt solve for initial conditions