73.3.48 problem 4.8 (g)

Internal problem ID [15082]
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 : 4.8 (g)
Date solved : Tuesday, January 28, 2025 at 07:30:06 AM
CAS classification : [_separable]

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

With initial conditions

\begin{align*} y \left (0\right )&=1 \end{align*}

✓ Solution by Maple

Time used: 0.349 (sec). Leaf size: 38

dsolve([(y(x)^2-1)*diff(y(x),x)=4*x*y(x),y(0) = 1],y(x), singsol=all)
 

\[ y = \frac {{\mathrm e}^{-2 x^{2}-\frac {1}{2}}}{\sqrt {-\frac {{\mathrm e}^{-4 x^{2}-1}}{\operatorname {LambertW}\left (-{\mathrm e}^{-4 x^{2}-1}\right )}}} \]

✓ Solution by Mathematica

Time used: 4.161 (sec). Leaf size: 25

DSolve[{(y[x]^2-1)*D[y[x],x]==4*x*y[x],{y[0]==1}},y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to -i \sqrt {W\left (-e^{-4 x^2-1}\right )} \]