73.1.22 problem 4 (iv)

Internal problem ID [19795]
Book : Elementary Differential Equations. By R.L.E. Schwarzenberger. Chapman and Hall. London. First Edition (1969)
Section : Chapter 3. Solutions of first-order equations. Exercises at page 47
Problem number : 4 (iv)
Date solved : Thursday, October 02, 2025 at 04:43:47 PM
CAS classification : [_linear]

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

✓ Maple. Time used: 0.002 (sec). Leaf size: 16

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

\[ x = t^{3} \left (\frac {1}{2}+{\mathrm e}^{\frac {1}{t^{2}}} c_1 \right ) \]

✓ Mathematica. Time used: 0.033 (sec). Leaf size: 23

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

\begin{align*} x(t)&\to \frac {1}{2} t^3 \left (1+2 c_1 e^{\frac {1}{t^2}}\right ) \end{align*}

✓ Sympy. Time used: 0.193 (sec). Leaf size: 17

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

\[ x{\left (t \right )} = t^{3} \left (C_{1} e^{\frac {1}{t^{2}}} + \frac {1}{2}\right ) \]