80.6.12 problem 10 (a)

Internal problem ID [18497]
Book : Elementary Differential Equations. By Thornton C. Fry. D Van Nostrand. NY. First Edition (1929)
Section : Chapter IV. Methods of solution: First order equations. section 33. Problems at page 91
Problem number : 10 (a)
Date solved : Thursday, March 13, 2025 at 12:08:39 PM
CAS classification : [_separable]

\begin{align*} v^{\prime }+2 u v&=2 u \end{align*}

✓ Maple. Time used: 0.001 (sec). Leaf size: 14

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

\[ v = 1+{\mathrm e}^{-u^{2}} c_{1} \]

✓ Mathematica. Time used: 0.05 (sec). Leaf size: 22

ode=D[v[u],u]+2*u*v[u]==2*u; 
ic={}; 
DSolve[{ode,ic},v[u],u,IncludeSingularSolutions->True]
 

\begin{align*} v(u)\to 1+c_1 e^{-u^2} \\ v(u)\to 1 \\ \end{align*}

✓ Sympy. Time used: 0.269 (sec). Leaf size: 10

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

\[ v{\left (u \right )} = C_{1} e^{- u^{2}} + 1 \]