Internal problem ID [15159]
Book: A book of problems in ordinary differential equations. M.L. KRASNOV, A.L. KISELYOV,
G.I. MARKARENKO. MIR, MOSCOW. 1983
Section: Section 12. Miscellaneous problems. Exercises page 93
Problem number: 297.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_separable]
\[ \boxed {\left (x -1\right ) \left (y^{2}-y+1\right )-\left (y-1\right ) \left (x^{2}+x +1\right ) y^{\prime }=0} \]
✓ Solution by Maple
Time used: 0.094 (sec). Leaf size: 2397
dsolve(((x-1)*(y(x)^2-y(x)+1))=((y(x)-1)*(x^2+x+1))*diff(y(x),x),y(x), singsol=all)
\[ \text {Expression too large to display} \]
✓ Solution by Mathematica
Time used: 0.578 (sec). Leaf size: 96
DSolve[((x-1)*(y[x]^2-y[x]+1))==((y[x]-1)*(x^2+x+1))*y'[x],y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \text {InverseFunction}\left [\frac {1}{2} \log \left (\text {$\#$1}^2-\text {$\#$1}+1\right )-\frac {\arctan \left (\frac {2 \text {$\#$1}-1}{\sqrt {3}}\right )}{\sqrt {3}}\&\right ]\left [-\sqrt {3} \arctan \left (\frac {2 x+1}{\sqrt {3}}\right )+\frac {1}{2} \log \left (x^2+x+1\right )+c_1\right ] \\ y(x)\to \sqrt [3]{-1} \\ y(x)\to -(-1)^{2/3} \\ \end{align*}