56.1.31 problem 32

Internal problem ID [8743]
Book : Own collection of miscellaneous problems
Section : section 1.0
Problem number : 32
Date solved : Sunday, March 30, 2025 at 01:29:23 PM
CAS classification : [[_homogeneous, `class C`], _rational, [_Abel, `2nd type`, `class A`]]

\begin{align*} 2 t +3 x+\left (x+2\right ) x^{\prime }&=0 \end{align*}

✓ Maple. Time used: 2.033 (sec). Leaf size: 30

ode:=2*t+3*x(t)+(x(t)+2)*diff(x(t),t) = 0; 
dsolve(ode,x(t), singsol=all);
 

\[ x = \frac {-\sqrt {4 \left (t -3\right ) c_1 +1}-1+\left (-4 t +8\right ) c_1}{2 c_1} \]

✓ Mathematica. Time used: 60.104 (sec). Leaf size: 1165

ode=2*t+3*x[t]+(x[t]+2)*D[x[t],t]==0; 
ic={}; 
DSolve[{ode,ic},x[t],t,IncludeSingularSolutions->True]
 

\begin{align*} \text {Solution too large to show}\end{align*}

✓ Sympy. Time used: 2.294 (sec). Leaf size: 44

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

\[ \left [ x{\left (t \right )} = 2 C_{1} - 2 t - 2 \sqrt {C_{1} \left (C_{1} - t + 3\right )} + 4, \ x{\left (t \right )} = 2 C_{1} - 2 t + 2 \sqrt {C_{1} \left (C_{1} - t + 3\right )} + 4\right ] \]