71.8.36 problem 12 (c)

Internal problem ID [14470]
Book : Ordinary Differential Equations by Charles E. Roberts, Jr. CRC Press. 2010
Section : Chapter 2. The Initial Value Problem. Exercises 2.4.4, page 115
Problem number : 12 (c)
Date solved : Tuesday, January 28, 2025 at 06:39:51 AM
CAS classification : [[_homogeneous, `class A`], _rational, _dAlembert]

\begin{align*} y^{\prime }&=\frac {x y}{x^{2}+y^{2}} \end{align*}

With initial conditions

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

✓ Solution by Maple

Time used: 1.871 (sec). Leaf size: 18

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

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

✓ Solution by Mathematica

Time used: 0.298 (sec). Leaf size: 16

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

\[ y(x)\to -\frac {x}{\sqrt {W\left (x^2\right )}} \]