4.2.23 problem 23

Internal problem ID [1151]
Book : Elementary differential equations and boundary value problems, 10th ed., Boyce and DiPrima
Section : Section 2.2. Page 48
Problem number : 23
Date solved : Tuesday, September 30, 2025 at 04:24:38 AM
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: 0.101 (sec). Leaf size: 16

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

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

✓ Mathematica. Time used: 0.101 (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]
 

\begin{align*} y(x)&\to -\frac {2}{x^2+4 x-2} \end{align*}

✓ Sympy. Time used: 0.113 (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)
 

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