34.2.6 problem 6

Internal problem ID [6036]
Book : A treatise on ordinary and partial differential equations by William Woolsey Johnson. 1913
Section : Chapter 2, Equations of the first order and degree. page 20
Problem number : 6
Date solved : Wednesday, March 05, 2025 at 12:10:16 AM
CAS classification : [_quadrature]

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

✓ Maple. Time used: 0.006 (sec). Leaf size: 32

ode:=diff(y(x),x)+b^2*y(x)^2 = a^2; 
dsolve(ode,y(x), singsol=all);
 

\[ y = -\frac {a \left ({\mathrm e}^{-2 a b \left (x +c_1 \right )}+1\right )}{b \left ({\mathrm e}^{-2 a b \left (x +c_1 \right )}-1\right )} \]

✓ Mathematica. Time used: 3.709 (sec). Leaf size: 37

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

\begin{align*} y(x)\to \frac {a \tanh (a b (x+c_1))}{b} \\ y(x)\to -\frac {a}{b} \\ y(x)\to \frac {a}{b} \\ \end{align*}

✓ Sympy. Time used: 0.825 (sec). Leaf size: 14

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

\[ y{\left (x \right )} = \frac {a}{b \tanh {\left (a b \left (C_{1} + x\right ) \right )}} \]