Internal problem ID [4596]
Book: Engineering Mathematics. By K. A. Stroud. 5th edition. Industrial press Inc. NY.
2001
Section: Program 24. First order differential equations. Further problems 24. page 1068
Problem number: 18.
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 {x -y-1+\left (4 y+x -1\right ) y^{\prime }=0} \end {gather*}
✓ Solution by Maple
Time used: 0.062 (sec). Leaf size: 29
dsolve((x-y(x)-1)+(4*y(x)+x-1)*diff(y(x),x)=0,y(x), singsol=all)
\[ y \relax (x ) = -\frac {\tan \left (\RootOf \left (\ln \left (\frac {1}{\cos \left (\textit {\_Z} \right )^{2}}\right )-\textit {\_Z} +2 \ln \left (x -1\right )+2 c_{1}\right )\right ) \left (x -1\right )}{2} \]
✓ Solution by Mathematica
Time used: 0.098 (sec). Leaf size: 58
DSolve[(x-y[x]-1)+(4*y[x]+x-1)*y'[x]==0,y[x],x,IncludeSingularSolutions -> True]
\[ \text {Solve}\left [2 \text {ArcTan}\left (\frac {2 y(x)-2 x+2}{4 y(x)+x-1}\right )+2 \log \left (\frac {4}{5} \left (\frac {4 y(x)^2}{(x-1)^2}+1\right )\right )+4 \log (x-1)+5 c_1=0,y(x)\right ] \]