Internal problem ID [3192]
Book: Ordinary differential equations and their solutions. By George Moseley Murphy.
1960
Section: Various 16
Problem number: 446.
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 (y+2 x \right ) y^{\prime }+x -2 y=0} \end {gather*}
✓ Solution by Maple
Time used: 0.01 (sec). Leaf size: 24
dsolve((2*x+y(x))*diff(y(x),x)+x-2*y(x) = 0,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: 0.037 (sec). Leaf size: 36
DSolve[(2 x+y[x])y'[x]+(x-2 y[x])==0,y[x],x,IncludeSingularSolutions -> True]
\[ \text {Solve}\left [2 \text {ArcTan}\left (\frac {y(x)}{x}\right )+\frac {1}{2} \log \left (\frac {y(x)^2}{x^2}+1\right )=-\log (x)+c_1,y(x)\right ] \]