Internal problem ID [3229]
Book: Ordinary differential equations and their solutions. By George Moseley Murphy.
1960
Section: Various 18
Problem number: 483.
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 +4 y\right ) y^{\prime }+4 x -y=0} \end {gather*}
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 24
dsolve((x+4*y(x))*diff(y(x),x)+4*x-y(x) = 0,y(x), singsol=all)
\[ y \relax (x ) = \tan \left (\RootOf \left (2 \ln \left (\frac {1}{\cos \left (\textit {\_Z} \right )^{2}}\right )+\textit {\_Z} +4 \ln \relax (x )+4 c_{1}\right )\right ) x \]
✓ Solution by Mathematica
Time used: 0.069 (sec). Leaf size: 32
DSolve[(x+4 y[x])y'[x]+4 x-y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\[ \text {Solve}\left [\text {ArcTan}\left (\frac {y(x)}{x}\right )+2 \log \left (\frac {y(x)^2}{x^2}+1\right )=-4 \log (x)+c_1,y(x)\right ] \]