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 : Monday, January 27, 2025 at 01:34:06 PM
CAS classification : [_quadrature]

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

✓ Solution by Maple

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

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

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

✓ Solution by Mathematica

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

DSolve[D[y[x],x]+b^2*y[x]^2==a^2,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*}