67.3.48 problem 4.8 (g)

Internal problem ID [16369]
Book : Ordinary Differential Equations. An introduction to the fundamentals. Kenneth B. Howell. second edition. CRC Press. FL, USA. 2020
Section : Chapter 4. SEPARABLE FIRST ORDER EQUATIONS. Additional exercises. page 90
Problem number : 4.8 (g)
Date solved : Thursday, October 02, 2025 at 01:22:50 PM
CAS classification : [_separable]

\begin{align*} \left (-1+y^{2}\right ) y^{\prime }&=4 y x \end{align*}

With initial conditions

\begin{align*} y \left (0\right )&=1 \\ \end{align*}

✓ Maple. Time used: 0.192 (sec). Leaf size: 38

ode:=(y(x)^2-1)*diff(y(x),x) = 4*x*y(x); 
ic:=[y(0) = 1]; 
dsolve([ode,op(ic)],y(x), singsol=all);
 

\[ y = \frac {{\mathrm e}^{-2 x^{2}-\frac {1}{2}}}{\sqrt {-\frac {{\mathrm e}^{-4 x^{2}-1}}{\operatorname {LambertW}\left (-{\mathrm e}^{-4 x^{2}-1}\right )}}} \]

✓ Mathematica. Time used: 2.661 (sec). Leaf size: 25

ode=(y[x]^2-1)*D[y[x],x]==4*x*y[x]; 
ic={y[0]==1}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to -i \sqrt {W\left (-e^{-4 x^2-1}\right )} \end{align*}

✗ Sympy

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

ValueError : Couldnt solve for initial conditions