8.36 problem 12 (c)

Internal problem ID [12734]

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).
ODE order: 1.
ODE degree: 1.

CAS Maple gives this as type [[_homogeneous, `class A`], _rational, _dAlembert]

\[ \boxed {y^{\prime }-\frac {x y}{x^{2}+y^{2}}=0} \] With initial conditions \begin {align*} [y \left (0\right ) = -1] \end {align*}

✓ Solution by Maple

Time used: 0.875 (sec). Leaf size: 13

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

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

✓ Solution by Mathematica

Time used: 0.443 (sec). Leaf size: 16

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

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