Internal problem ID [5323]
Book: An introduction to Ordinary Differential Equations. Earl A. Coddington. Dover. NY
1961
Section: Chapter 5. Existence and uniqueness of solutions to first order equations. Page
190
Problem number: 5(b).
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 {y^{\prime }-\frac {2 x +3 y+1}{x -2 y-1}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.266 (sec). Leaf size: 59
dsolve(diff(y(x),x)=(2*x+3*y(x)+1)/(x-2*y(x)-1),y(x), singsol=all)
\[ y \relax (x ) = -\frac {5}{14}-\frac {x}{2}+\frac {\sqrt {3}\, \left (7 x -1\right ) \tan \left (\RootOf \left (\sqrt {3}\, \ln \left (\frac {3 \left (7 x -1\right )^{2}}{4}+\frac {3 \left (\tan ^{2}\left (\textit {\_Z} \right )\right ) \left (7 x -1\right )^{2}}{4}\right )+2 \sqrt {3}\, c_{1}-4 \textit {\_Z} \right )\right )}{14} \]
✓ Solution by Mathematica
Time used: 0.119 (sec). Leaf size: 85
DSolve[y'[x]==(2*x+3*y[x]+1)/(x-2*y[x]-1),y[x],x,IncludeSingularSolutions -> True]
\[ \text {Solve}\left [32 \sqrt {3} \text {ArcTan}\left (\frac {4 y(x)+5 x+1}{\sqrt {3} (-2 y(x)+x-1)}\right )=3 \left (8 \log \left (\frac {4 \left (7 x^2+7 y(x)^2+(7 x+5) y(x)+x+1\right )}{(1-7 x)^2}\right )+16 \log (7 x-1)+7 c_1\right ),y(x)\right ] \]