20.4.41 problem Problem 59

Internal problem ID [3676]
Book : Differential equations and linear algebra, Stephen W. Goode and Scott A Annin. Fourth edition, 2015
Section : Chapter 1, First-Order Differential Equations. Section 1.8, Change of Variables. page 79
Problem number : Problem 59
Date solved : Tuesday, March 04, 2025 at 05:06:10 PM
CAS classification : [[_1st_order, _with_linear_symmetries], _Riccati]

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

With initial conditions

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

✓ Maple. Time used: 0.120 (sec). Leaf size: 20

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

\[ y \left (x \right ) = \frac {-x^{3}+x -1}{x^{2}-1} \]

✓ Mathematica. Time used: 0.155 (sec). Leaf size: 21

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

\[ y(x)\to \frac {-x^3+x-1}{x^2-1} \]

✓ Sympy. Time used: 0.315 (sec). Leaf size: 14

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

\[ y{\left (x \right )} = \frac {- x^{3} + x - 1}{x^{2} - 1} \]