Internal problem ID [2197]
Book: Differential equations and linear algebra, Stephen W. Goode and Scott A Annin. Fourth edition,
2015
Section: Chapter 1, First-Order Differential Equations. Section 1.8, Change of Variables. page
79
Problem number: Problem 60.
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 {x +2 y-1}{2 x -y+3}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.031 (sec). Leaf size: 31
dsolve(diff(y(x),x)=(x+2*y(x)-1)/(2*x-y(x)+3),y(x), singsol=all)
\[ y \relax (x ) = 1-\tan \left (\RootOf \left (4 \textit {\_Z} +\ln \left (\frac {1}{\cos \left (\textit {\_Z} \right )^{2}}\right )+2 \ln \left (x +1\right )+2 c_{1}\right )\right ) \left (x +1\right ) \]
✓ Solution by Mathematica
Time used: 0.064 (sec). Leaf size: 68
DSolve[y'[x]==(x+2*y[x]-1)/(2*x-y[x]+3),y[x],x,IncludeSingularSolutions -> True]
\[ \text {Solve}\left [32 \text {ArcTan}\left (\frac {-2 y(x)-x+1}{-y(x)+2 x+3}\right )+8 \log \left (\frac {x^2+y(x)^2-2 y(x)+2 x+2}{5 (x+1)^2}\right )+16 \log (x+1)+5 c_1=0,y(x)\right ] \]