Internal problem ID [2606]
Book: Differential equations with applications and historial notes, George F. Simmons,
1971
Section: Chapter 2, End of chapter, page 61
Problem number: 3.
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 {2 x +3 y+1+\left (2 y-3 x +5\right ) y^{\prime }=0} \end {gather*}
✓ Solution by Maple
Time used: 0.028 (sec). Leaf size: 31
dsolve((2*x+3*y(x)+1)+(2*y(x)-3*x+5)*diff(y(x),x)=0,y(x), singsol=all)
\[ y \relax (x ) = -1-\tan \left (\RootOf \left (3 \textit {\_Z} +\ln \left (\frac {1}{\cos \left (\textit {\_Z} \right )^{2}}\right )+2 \ln \left (x -1\right )+2 c_{1}\right )\right ) \left (x -1\right ) \]
✓ Solution by Mathematica
Time used: 0.063 (sec). Leaf size: 68
DSolve[(2*x+3*y[x]+1)+(2*y[x]-3*x+5)*y'[x]==0,y[x],x,IncludeSingularSolutions -> True]
\[ \text {Solve}\left [54 \text {ArcTan}\left (\frac {3 y(x)+2 x+1}{2 y(x)-3 x+5}\right )+18 \log \left (\frac {4 \left (x^2+y(x)^2+2 y(x)-2 x+2\right )}{13 (x-1)^2}\right )+36 \log (x-1)+13 c_1=0,y(x)\right ] \]