90.3.29 problem 29

Internal problem ID [25093]
Book : Ordinary Differential Equations. By William Adkins and Mark G Davidson. Springer. NY. 2010. ISBN 978-1-4614-3617-1
Section : Chapter 1. First order differential equations. Exercises at page 41
Problem number : 29
Date solved : Thursday, October 02, 2025 at 11:49:59 PM
CAS classification : [_separable]

\begin{align*} \frac {\left (u^{2}+1\right ) y^{\prime }}{y}&=u \end{align*}

With initial conditions

\begin{align*} y \left (0\right )&=2 \\ \end{align*}

✓ Maple. Time used: 0.026 (sec). Leaf size: 13

ode:=(u^2+1)/y(u)*diff(y(u),u) = u; 
ic:=[y(0) = 2]; 
dsolve([ode,op(ic)],y(u), singsol=all);
 

\[ y = 2 \sqrt {u^{2}+1} \]

✓ Mathematica. Time used: 0.025 (sec). Leaf size: 16

ode=(u^2+1)/y[u]*D[y[u],{u,1}] ==u; 
ic={y[0]==2}; 
DSolve[{ode,ic},y[u],u,IncludeSingularSolutions->True]
 

\begin{align*} y(u)&\to 2 \sqrt {u^2+1} \end{align*}

✗ Sympy

from sympy import * 
u = symbols("u") 
y = Function("y") 
ode = Eq(-u + (u**2 + 1)*Derivative(y(t), t)/y(u),0) 
ics = {y(0): 2} 
dsolve(ode,func=y(u),ics=ics)
 

ValueError : Couldnt solve for initial conditions