Internal problem ID [4184]
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.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_quadrature]
Solve \begin {gather*} \boxed {y^{\prime }+b^{2} y^{2}-a^{2}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 40
dsolve(diff(y(x),x)+b^2*y(x)^2=a^2,y(x), singsol=all)
\[ y \relax (x ) = -\frac {a \left ({\mathrm e}^{-2 b x a -2 c_{1} a b}+1\right )}{b \left ({\mathrm e}^{-2 b x a -2 c_{1} a b}-1\right )} \]
✓ Solution by Mathematica
Time used: 2.523 (sec). Leaf size: 37
DSolve[y'[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*}