Internal problem ID [7802]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 1, linear first order
Problem number: 222.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, class C], _rational, [_Abel, 2nd type, class A]]
Solve \begin {gather*} \boxed {\left (2 y+x +7\right ) y^{\prime }-y+2 x +4=0} \end {gather*}
✓ Solution by Maple
Time used: 0.036 (sec). Leaf size: 31
dsolve((2*y(x)+x+7)*diff(y(x),x)-y(x)+2*x+4=0,y(x), singsol=all)
\[ y \relax (x ) = -2-\tan \left (\RootOf \left (\ln \left (\frac {1}{\cos \left (\textit {\_Z} \right )^{2}}\right )-\textit {\_Z} +2 \ln \left (3+x \right )+2 c_{1}\right )\right ) \left (3+x \right ) \]
✓ Solution by Mathematica
Time used: 0.059 (sec). Leaf size: 65
DSolve[(2*y[x]+x+7)*y'[x]-y[x]+2*x+4==0,y[x],x,IncludeSingularSolutions -> True]
\[ \operatorname {Solve}\left [2 \operatorname {ArcTan}\left (\frac {y(x)-2 (x+2)}{2 y(x)+x+7}\right )+2 \log \left (\frac {4 \left (x^2+y(x)^2+4 y(x)+6 x+13\right )}{5 (x+3)^2}\right )+4 \log (x+3)+5 c_1=0,y(x)\right ] \]