15.6.23 problem 23

Internal problem ID [2980]
Book : Differential Equations by Alfred L. Nelson, Karl W. Folley, Max Coral. 3rd ed. DC heath. Boston. 1964
Section : Exercise 10, page 41
Problem number : 23
Date solved : Monday, January 27, 2025 at 07:05:22 AM
CAS classification : [[_homogeneous, `class G`], _rational]

\begin{align*} y+2 \left (x -2 y^{2}\right ) y^{\prime }&=0 \end{align*}

With initial conditions

\begin{align*} y \left (2\right )&=-1 \end{align*}

✓ Solution by Maple

Time used: 0.112 (sec). Leaf size: 41

dsolve([y(x)+2*(x-2*y(x)^2)*diff(y(x),x)=0,y(2) = -1],y(x), singsol=all)
 

\begin{align*} y &= -\frac {\sqrt {-2 \sqrt {x^{2}-4}+2 x}}{2} \\ y &= -\frac {\sqrt {2 \sqrt {x^{2}-4}+2 x}}{2} \\ \end{align*}

✓ Solution by Mathematica

Time used: 2.129 (sec). Leaf size: 55

DSolve[{y[x]+2*(x-2*y[x]^2)*D[y[x],x]==0,{y[2]==-1}},y[x],x,IncludeSingularSolutions -> True]
 

\begin{align*} y(x)\to -\frac {\sqrt {x-\sqrt {x^2-4}}}{\sqrt {2}} \\ y(x)\to -\frac {\sqrt {\sqrt {x^2-4}+x}}{\sqrt {2}} \\ \end{align*}