Internal problem ID [13346]
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).
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_separable]
\[ \boxed {\left (y^{2}-1\right ) y^{\prime }-4 y x=0} \] With initial conditions \begin {align*} [y \left (0\right ) = 1] \end {align*}
✓ Solution by Maple
Time used: 0.203 (sec). Leaf size: 25
dsolve([(y(x)^2-1)*diff(y(x),x)=4*x*y(x),y(0) = 1],y(x), singsol=all)
\[ y \left (x \right ) = \frac {{\mathrm e}^{-2 x^{2}-\frac {1}{2}}}{\sqrt {-\frac {{\mathrm e}^{-4 x^{2}-1}}{\operatorname {LambertW}\left (-{\mathrm e}^{-4 x^{2}-1}\right )}}} \]
✓ Solution by Mathematica
Time used: 4.197 (sec). Leaf size: 25
DSolve[{(y[x]^2-1)*y'[x]==4*x*y[x],{y[0]==1}},y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to -i \sqrt {W\left (-e^{-4 x^2-1}\right )} \]