Internal problem ID [13117]
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.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_quadrature]
\[ \boxed {\left (y^{2}-4\right ) y^{\prime }-y=0} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 25
dsolve((y(x)^2-4)*diff(y(x),x)=y(x),y(x), singsol=all)
\[ y = {\mathrm e}^{-\frac {\operatorname {LambertW}\left (-\frac {{\mathrm e}^{-\frac {x}{2}-\frac {c_{1}}{2}}}{4}\right )}{2}-\frac {x}{4}-\frac {c_{1}}{4}} \]
✓ Solution by Mathematica
Time used: 32.653 (sec). Leaf size: 246
DSolve[(y[x]^2-4)*y'[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*}