Internal problem ID [12413]
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 (b).
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 ) = 0] \end {align*}
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 5
dsolve([diff(y(x),x)=x*y(x)/(x^2+y(x)^2),y(0) = 0],y(x), singsol=all)
\[ y \left (x \right ) = 0 \]
✓ Solution by Mathematica
Time used: 0.002 (sec). Leaf size: 6
DSolve[{y'[x]==x*y[x]/(x^2+y[x]^2),{y[0]==0}},y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to 0 \]