Internal problem ID [872]
Book: Elementary differential equations with boundary value problems. William F. Trench.
Brooks/Cole 2001
Section: Chapter 1, Introduction. Section 1.2 Page 14
Problem number: 2(d).
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_separable]
\[ \boxed {2 y^{\prime }+x \left (-1+y^{2}\right )=0} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 14
dsolve(2*diff(y(x),x) +x*(y(x)^2-1)= 0,y(x), singsol=all)
\[ y \left (x \right ) = \tanh \left (\frac {x^{2}}{4}+\frac {c_{1}}{2}\right ) \]
✓ Solution by Mathematica
Time used: 0.242 (sec). Leaf size: 52
DSolve[2*y'[x] +x*(y[x]^2-1)== 0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {e^{\frac {x^2}{2}}-e^{2 c_1}}{e^{\frac {x^2}{2}}+e^{2 c_1}} y(x)\to -1 y(x)\to 1 \end{align*}