Internal problem ID [15035]
Book: A book of problems in ordinary differential equations. M.L. KRASNOV, A.L. KISELYOV,
G.I. MARKARENKO. MIR, MOSCOW. 1983
Section: Section 6. Linear equations of the first order. The Bernoulli equation. Exercises page
54
Problem number: 133.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, `class G`], _rational]
\[ \boxed {\left (-y^{2}+2 x \right ) y^{\prime }-2 y=0} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 31
dsolve((2*x-y(x)^2)*diff(y(x),x)=2*y(x),y(x), singsol=all)
\begin{align*} y \left (x \right ) &= c_{1} -\sqrt {c_{1}^{2}-2 x} \\ y \left (x \right ) &= c_{1} +\sqrt {c_{1}^{2}-2 x} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.253 (sec). Leaf size: 46
DSolve[(2*x-y[x]^2)*y'[x]==2*y[x],y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to c_1-\sqrt {-2 x+c_1{}^2} \\ y(x)\to \sqrt {-2 x+c_1{}^2}+c_1 \\ y(x)\to 0 \\ \end{align*}