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`]]
\[ \boxed {\left (x -y\right ) y^{\prime }-y=x} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 24
dsolve((x-y(x))*diff(y(x),x) = x+y(x),y(x), singsol=all)
\[ y \left (x \right ) = \tan \left (\operatorname {RootOf}\left (-2 \textit {\_Z} +\ln \left (\frac {1}{\cos \left (\textit {\_Z} \right )^{2}}\right )+2 \ln \left (x \right )+2 c_{1} \right )\right ) x \]
✓ Solution by Mathematica
Time used: 0.031 (sec). Leaf size: 36
DSolve[(x-y[x])*y'[x] == x+y[x],y[x],x,IncludeSingularSolutions -> True]
\[ \text {Solve}\left [\frac {1}{2} \log \left (\frac {y(x)^2}{x^2}+1\right )-\arctan \left (\frac {y(x)}{x}\right )=-\log (x)+c_1,y(x)\right ] \]