35.4.9 problem 9

Internal problem ID [6127]
Book : Mathematical Methods in the Physical Sciences. third edition. Mary L. Boas. John Wiley. 2006
Section : Chapter 8, Ordinary differential equations. Section 4. OTHER METHODS FOR FIRST-ORDER EQUATIONS. page 406
Problem number : 9
Date solved : Monday, January 27, 2025 at 01:37:40 PM
CAS classification : [[_homogeneous, `class A`], _rational, _dAlembert]

\begin{align*} y x +\left (y^{2}-x^{2}\right ) y^{\prime }&=0 \end{align*}

✓ Solution by Maple

Time used: 0.013 (sec). Leaf size: 19

dsolve(x*y(x)+(y(x)^2-x^2)*diff(y(x),x)=0,y(x), singsol=all)
 

\[ y = \sqrt {-\frac {1}{\operatorname {LambertW}\left (-c_1 \,x^{2}\right )}}\, x \]

✓ Solution by Mathematica

Time used: 7.968 (sec). Leaf size: 60

DSolve[x*y[x]+(y[x]^2-x^2)*D[y[x],x]==0,y[x],x,IncludeSingularSolutions -> True]
 

\begin{align*} y(x)\to -\frac {i x}{\sqrt {W\left (-e^{-3-2 c_1} x^2\right )}} \\ y(x)\to \frac {i x}{\sqrt {W\left (-e^{-3-2 c_1} x^2\right )}} \\ y(x)\to 0 \\ \end{align*}