73.1.18 problem 3 (vi)

Internal problem ID [19791]
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 : 3 (vi)
Date solved : Thursday, October 02, 2025 at 04:43:41 PM
CAS classification : [_exact, _rational, [_1st_order, `_with_symmetry_[F(x),G(x)]`], [_Abel, `2nd type`, `class A`]]

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

✓ Maple. Time used: 0.004 (sec). Leaf size: 51

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

\begin{align*} x &= 3 t -\frac {\sqrt {-6 t^{3}+99 t^{2}+18 c_1}}{3} \\ x &= 3 t +\frac {\sqrt {-6 t^{3}+99 t^{2}+18 c_1}}{3} \\ \end{align*}

✓ Mathematica. Time used: 0.099 (sec). Leaf size: 67

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

\begin{align*} x(t)&\to 3 t-i \sqrt {\frac {2 t^3}{3}-11 t^2-c_1}\\ x(t)&\to 3 t+i \sqrt {\frac {2 t^3}{3}-11 t^2-c_1} \end{align*}

✗ Sympy

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

Timed Out