Internal problem ID [15145]
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: 283.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_1st_order, _with_exponential_symmetries]]
\[ \boxed {y^{\prime }-\frac {1}{2 x -y^{2}}=0} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 24
dsolve(diff(y(x),x)=1/(2*x-y(x)^2),y(x), singsol=all)
\[ x -\frac {y^{2}}{2}-\frac {y}{2}-\frac {1}{4}-{\mathrm e}^{2 y} c_{1} = 0 \]
✓ Solution by Mathematica
Time used: 0.135 (sec). Leaf size: 31
DSolve[y'[x]==1/(2*x-y[x]^2),y[x],x,IncludeSingularSolutions -> True]
\[ \text {Solve}\left [x=\frac {1}{4} \left (2 y(x)^2+2 y(x)+1\right )+c_1 e^{2 y(x)},y(x)\right ] \]