5.4 problem 4

Internal problem ID [82]

Book: Differential equations and linear algebra, 3rd ed., Edwards and Penney
Section: Section 1.6, Substitution methods and exact equations. Page 74
Problem number: 4.
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 {\left (x -y\right ) y^{\prime }-x -y=0} \end {gather*}

Solution by Maple

Time used: 0.016 (sec). Leaf size: 24

dsolve((x-y(x))*diff(y(x),x) = x+y(x),y(x), singsol=all)
 

\[ y \relax (x ) = \tan \left (\RootOf \left (-2 \textit {\_Z} +\ln \left (\frac {1}{\cos \left (\textit {\_Z} \right )^{2}}\right )+2 \ln \relax (x )+2 c_{1}\right )\right ) x \]

Solution by Mathematica

Time used: 0.033 (sec). Leaf size: 36

DSolve[(x-y[x])*y'[x] == x+y[x],y[x],x,IncludeSingularSolutions -> True]
 

\[ \text {Solve}\left [\frac {1}{2} \log \left (\frac {y(x)^2}{x^2}+1\right )-\text {ArcTan}\left (\frac {y(x)}{x}\right )=-\log (x)+c_1,y(x)\right ] \]