76.1.31 problem 31

Internal problem ID [17259]
Book : Differential equations. An introduction to modern methods and applications. James Brannan, William E. Boyce. Third edition. Wiley 2015
Section : Chapter 2. First order differential equations. Section 2.1 (Separable equations). Problems at page 44
Problem number : 31
Date solved : Monday, March 31, 2025 at 03:47:38 PM
CAS classification : [_separable]

\begin{align*} y^{\prime }&=2 y^{2}+x y^{2} \end{align*}

With initial conditions

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

✓ Maple. Time used: 0.102 (sec). Leaf size: 16

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

\[ y = -\frac {2}{x^{2}+4 x -2} \]

✓ Mathematica. Time used: 0.156 (sec). Leaf size: 17

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

\[ y(x)\to -\frac {2}{x^2+4 x-2} \]

✓ Sympy. Time used: 0.184 (sec). Leaf size: 14

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

\[ y{\left (x \right )} = - \frac {2}{x^{2} + 4 x - 2} \]