Internal problem ID [13332]
Book: Ordinary Differential Equations. An introduction to the fundamentals. Kenneth B. Howell.
second edition. CRC Press. FL, USA. 2020
Section: Chapter 4. SEPARABLE FIRST ORDER EQUATIONS. Additional exercises. page
90
Problem number: 4.7 (h).
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_separable]
\[ \boxed {\left (y^{2}-1\right ) y^{\prime }-4 y^{2} x=0} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 59
dsolve((y(x)^2-1)*diff(y(x),x)=4*x*y(x)^2,y(x), singsol=all)
\begin{align*} y \left (x \right ) &= x^{2}+2 c_{1} -\sqrt {x^{4}+4 c_{1} x^{2}+4 c_{1}^{2}-1} \\ y \left (x \right ) &= x^{2}+2 c_{1} +\sqrt {x^{4}+4 c_{1} x^{2}+4 c_{1}^{2}-1} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.273 (sec). Leaf size: 84
DSolve[(y[x]^2-1)*y'[x]==4*x*y[x]^2,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {1}{2} \left (2 x^2-\sqrt {4 x^4+4 c_1 x^2-4+c_1{}^2}+c_1\right ) \\ y(x)\to \frac {1}{2} \left (2 x^2+\sqrt {4 x^4+4 c_1 x^2-4+c_1{}^2}+c_1\right ) \\ y(x)\to 0 \\ \end{align*}