73.7.15 problem 15

Internal problem ID [15173]
Book : Ordinary Differential Equations. An introduction to the fundamentals. Kenneth B. Howell. second edition. CRC Press. FL, USA. 2020
Section : Chapter 8. Review exercises for part of part II. page 143
Problem number : 15
Date solved : Tuesday, January 28, 2025 at 07:40:01 AM
CAS classification : [_quadrature]

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

✓ Solution by Maple

Time used: 0.036 (sec). Leaf size: 39

dsolve((y(x)^2-4)*diff(y(x),x)=y(x),y(x), singsol=all)
 

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

✓ Solution by Mathematica

Time used: 28.001 (sec). Leaf size: 246

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

\begin{align*} y(x)\to -2 i \sqrt {W\left (-\frac {1}{4} \sqrt [4]{e^{-2 (x+c_1)}}\right )} \\ y(x)\to 2 i \sqrt {W\left (-\frac {1}{4} \sqrt [4]{e^{-2 (x+c_1)}}\right )} \\ y(x)\to -2 i \sqrt {W\left (-\frac {1}{4} i \sqrt [4]{e^{-2 (x+c_1)}}\right )} \\ y(x)\to 2 i \sqrt {W\left (-\frac {1}{4} i \sqrt [4]{e^{-2 (x+c_1)}}\right )} \\ y(x)\to -2 i \sqrt {W\left (\frac {1}{4} i \sqrt [4]{e^{-2 (x+c_1)}}\right )} \\ y(x)\to 2 i \sqrt {W\left (\frac {1}{4} i \sqrt [4]{e^{-2 (x+c_1)}}\right )} \\ y(x)\to -2 i \sqrt {W\left (\frac {1}{4} \sqrt [4]{e^{-2 (x+c_1)}}\right )} \\ y(x)\to 2 i \sqrt {W\left (\frac {1}{4} \sqrt [4]{e^{-2 (x+c_1)}}\right )} \\ y(x)\to 0 \\ \end{align*}