64.5.6 problem 6

Internal problem ID [13248]
Book : Differential Equations by Shepley L. Ross. Third edition. John Willey. New Delhi. 2004.
Section : Chapter 2, section 2.3 (Linear equations). Exercises page 56
Problem number : 6
Date solved : Monday, March 31, 2025 at 07:43:25 AM
CAS classification : [_separable]

\begin{align*} \left (u^{2}+1\right ) v^{\prime }+4 u v&=3 u \end{align*}

✓ Maple. Time used: 0.001 (sec). Leaf size: 15

ode:=(u^2+1)*diff(v(u),u)+4*u*v(u) = 3*u; 
dsolve(ode,v(u), singsol=all);
 

\[ v = \frac {3}{4}+\frac {c_1}{\left (u^{2}+1\right )^{2}} \]

✓ Mathematica. Time used: 0.045 (sec). Leaf size: 38

ode=(u^2+1)*D[ v[u],u]+4*u*v[u]==3*u; 
ic={}; 
DSolve[{ode,ic},v[u],u,IncludeSingularSolutions->True]
 

\begin{align*} v(u)\to \frac {3 u^4+6 u^2+4 c_1}{4 \left (u^2+1\right )^2} \\ v(u)\to \frac {3}{4} \\ \end{align*}

✓ Sympy. Time used: 0.323 (sec). Leaf size: 19

from sympy import * 
u = symbols("u") 
v = Function("v") 
ode = Eq(4*u*v(u) - 3*u + (u**2 + 1)*Derivative(v(u), u),0) 
ics = {} 
dsolve(ode,func=v(u),ics=ics)
 

\[ v{\left (u \right )} = \frac {C_{1}}{4 \left (u^{4} + 2 u^{2} + 1\right )} + \frac {3}{4} \]