77.1.31 problem 48 (page 56)

Internal problem ID [17921]
Book : V.V. Stepanov, A course of differential equations (in Russian), GIFML. Moscow (1958)
Section : All content
Problem number : 48 (page 56)
Date solved : Tuesday, January 28, 2025 at 11:12:43 AM
CAS classification : [[_homogeneous, `class G`], _rational]

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

✓ Solution by Maple

Time used: 0.552 (sec). Leaf size: 81

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

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

✓ Solution by Mathematica

Time used: 2.236 (sec). Leaf size: 119

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

\begin{align*} y(x)\to -\sqrt {-x-\sqrt {2} \sqrt {x^2+c_1}} \\ y(x)\to \sqrt {-x-\sqrt {2} \sqrt {x^2+c_1}} \\ y(x)\to -\sqrt {-x+\sqrt {2} \sqrt {x^2+c_1}} \\ y(x)\to \sqrt {-x+\sqrt {2} \sqrt {x^2+c_1}} \\ \end{align*}