73.3.34 problem 4.7 (h)

Internal problem ID [15068]
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)
Date solved : Tuesday, January 28, 2025 at 07:29:23 AM
CAS classification : [_separable]

\begin{align*} \left (-1+y^{2}\right ) y^{\prime }&=4 x y^{2} \end{align*}

✓ Solution by Maple

Time used: 0.005 (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 &= x^{2}+2 c_{1} -\sqrt {x^{4}+4 c_{1} x^{2}+4 c_{1}^{2}-1} \\ y &= 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: 0.331 (sec). Leaf size: 84

DSolve[(y[x]^2-1)*D[y[x],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*}