75.12.9 problem 283

Internal problem ID [16875]
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
Date solved : Tuesday, January 28, 2025 at 09:38:44 AM
CAS classification : [[_1st_order, _with_exponential_symmetries]]

\begin{align*} y^{\prime }&=\frac {1}{2 x -y^{2}} \end{align*}

✓ Solution by Maple

Time used: 0.007 (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: 0.151 (sec). Leaf size: 42

DSolve[D[y[x],x]==1/(2*x-y[x]^2),y[x],x,IncludeSingularSolutions -> True]
 

\[ \text {Solve}\left [x=e^{2 y(x)} \int _1^{y(x)}-e^{-2 K[1]} K[1]^2dK[1]+c_1 e^{2 y(x)},y(x)\right ] \]