Internal problem ID [13063]
Book: Ordinary Differential Equations. An introduction to the fundamentals. Kenneth B. Howell.
second edition. CRC Press. FL, USA. 2020
Section: Chapter 6. Simplifying through simplifiction. Additional exercises. page 114
Problem number: 6.4.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, `class A`], _rational, [_Abel, `2nd type`, `class A`]]
\[ \boxed {y^{\prime }-\frac {x -y}{x +y}=0} \] With initial conditions \begin {align*} [y \left (0\right ) = 3] \end {align*}
✓ Solution by Maple
Time used: 0.547 (sec). Leaf size: 19
dsolve([diff(y(x),x)=(x-y(x))/(x+y(x)),y(0) = 3],y(x), singsol=all)
\[ y = -x +\sqrt {2 x^{2}+9} \]
✓ Solution by Mathematica
Time used: 0.434 (sec). Leaf size: 20
DSolve[{y'[x]==(x-y[x])/(x+y[x]),{y[0]==3}},y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \sqrt {2 x^2+9}-x \]