Internal problem ID [12412]
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 (a).
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: 0.578 (sec). Leaf size: 11
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: 10.851 (sec). Leaf size: 15
DSolve[{y'[x]==x*y[x]/(x^2+y[x]^2),{y[0]==1}},y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \frac {x}{\sqrt {W\left (x^2\right )}} \]