Internal problem ID [5501]
Book: Differential Equations: Theory, Technique, and Practice by George Simmons, Steven Krantz.
McGraw-Hill NY. 2007. 1st Edition.
Section: Chapter 1. What is a differential equation. Problems for Review and Discovery. Page
53
Problem number: 1(f).
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, class A], _rational, [_Abel, 2nd type, class A]]
Solve \begin {gather*} \boxed {y^{\prime }-\frac {x +2 y}{-y+2 x}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.031 (sec). Leaf size: 24
dsolve(diff(y(x),x)=(x+2*y(x))/(2*x-y(x)),y(x), singsol=all)
\[ y \relax (x ) = \tan \left (\RootOf \left (-4 \textit {\_Z} +\ln \left (\frac {1}{\cos \left (\textit {\_Z} \right )^{2}}\right )+2 \ln \relax (x )+2 c_{1}\right )\right ) x \]
✗ Solution by Mathematica
Time used: 0.0 (sec). Leaf size: 0
DSolve[y'[x]==(x+2*y[x]^2)/(2*x-y[x]),y[x],x,IncludeSingularSolutions -> True]
Not solved