75.6.9 problem 133

Internal problem ID [16765]
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
Date solved : Tuesday, January 28, 2025 at 09:21:48 AM
CAS classification : [[_homogeneous, `class G`], _rational]

\begin{align*} \left (2 x -y^{2}\right ) y^{\prime }&=2 y \end{align*}

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 31

dsolve((2*x-y(x)^2)*diff(y(x),x)=2*y(x),y(x), singsol=all)
 

\begin{align*} y &= c_{1} -\sqrt {c_{1}^{2}-2 x} \\ y &= c_{1} +\sqrt {c_{1}^{2}-2 x} \\ \end{align*}

✓ Solution by Mathematica

Time used: 0.274 (sec). Leaf size: 46

DSolve[(2*x-y[x]^2)*D[y[x],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*}