89.2.32 problem 34

Internal problem ID [24297]
Book : A short course in Differential Equations. Earl D. Rainville. Second edition. 1958. Macmillan Publisher, NY. CAT 58-5010
Section : Chapter 2. Equations of the first order and first degree. Exercises at page 27
Problem number : 34
Date solved : Thursday, October 02, 2025 at 10:10:49 PM
CAS classification : [[_homogeneous, `class A`], _rational, _Bernoulli]

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

With initial conditions

\begin{align*} v \left (1\right )&=2 \\ \end{align*}

✓ Maple. Time used: 0.033 (sec). Leaf size: 18

ode:=v(x)*(3*x+2*v(x))-x^2*diff(v(x),x) = 0; 
ic:=[v(1) = 2]; 
dsolve([ode,op(ic)],v(x), singsol=all);
 

\[ v = -\frac {2 x^{3}}{2 x^{2}-3} \]

✓ Mathematica. Time used: 0.098 (sec). Leaf size: 19

ode=v[x]*( 3*x+2*v[x] )-( x^2 )*D[v[x],x]==0; 
ic={v[1]==2}; 
DSolve[{ode,ic},v[x],x,IncludeSingularSolutions->True]
 

\begin{align*} v(x)&\to \frac {2 x^3}{3-2 x^2} \end{align*}

✓ Sympy. Time used: 0.126 (sec). Leaf size: 12

from sympy import * 
x = symbols("x") 
v = Function("v") 
ode = Eq(-x**2*Derivative(v(x), x) + (3*x + 2*v(x))*v(x),0) 
ics = {v(1): 2} 
dsolve(ode,func=v(x),ics=ics)
 

\[ v{\left (x \right )} = \frac {x^{3}}{\frac {3}{2} - x^{2}} \]