89.2.7 problem 7

Internal problem ID [24272]
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 : 7
Date solved : Thursday, October 02, 2025 at 10:05:10 PM
CAS classification : [[_homogeneous, `class A`], _rational, [_Abel, `2nd type`, `class A`]]

\begin{align*} 5 v-u +\left (3 v-7 u \right ) v^{\prime }&=0 \end{align*}

✓ Maple. Time used: 0.077 (sec). Leaf size: 47

ode:=5*v(u)-u+(3*v(u)-7*u)*diff(v(u),u) = 0; 
dsolve(ode,v(u), singsol=all);
 

\begin{align*} v &= \frac {-6 u c_1 -\sqrt {-48 u c_1 +1}+1}{18 c_1} \\ v &= \frac {-6 u c_1 +1+\sqrt {-48 u c_1 +1}}{18 c_1} \\ \end{align*}

✓ Mathematica. Time used: 0.559 (sec). Leaf size: 80

ode=(5*v[u]-u)+(3*v[u]-7*u)*D[v[u],u]==0; 
ic={}; 
DSolve[{ode,ic},v[u],u,IncludeSingularSolutions->True]
 

\begin{align*} v(u)&\to \frac {1}{18} \left (-6 u-e^{\frac {c_1}{2}} \sqrt {48 u+e^{c_1}}-e^{c_1}\right )\\ v(u)&\to \frac {1}{18} \left (-6 u+e^{\frac {c_1}{2}} \sqrt {48 u+e^{c_1}}-e^{c_1}\right ) \end{align*}

✓ Sympy. Time used: 1.317 (sec). Leaf size: 42

from sympy import * 
u = symbols("u") 
v = Function("v") 
ode = Eq(-u + (-7*u + 3*v(u))*Derivative(v(u), u) + 5*v(u),0) 
ics = {} 
dsolve(ode,func=v(u),ics=ics)
 

\[ \left [ v{\left (u \right )} = - \frac {C_{1}}{18} - \frac {u}{3} - \frac {\sqrt {C_{1} \left (C_{1} + 48 u\right )}}{18}, \ v{\left (u \right )} = - \frac {C_{1}}{18} - \frac {u}{3} + \frac {\sqrt {C_{1} \left (C_{1} + 48 u\right )}}{18}\right ] \]