60.1.241 problem 242

Internal problem ID [10255]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 1, linear first order
Problem number : 242
Date solved : Monday, January 27, 2025 at 06:41:56 PM
CAS classification : [_separable]

\begin{align*} 2 x y y^{\prime }+2 y^{2}+1&=0 \end{align*}

✓ Solution by Maple

Time used: 0.004 (sec). Leaf size: 39

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

\begin{align*} y &= -\frac {\sqrt {-2 x^{2}+4 c_{1}}}{2 x} \\ y &= \frac {\sqrt {-2 x^{2}+4 c_{1}}}{2 x} \\ \end{align*}

✓ Solution by Mathematica

Time used: 0.334 (sec). Leaf size: 128

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

\begin{align*} y(x)\to -\frac {\sqrt {-x^2+e^{4 c_1}}}{\sqrt {2} x} \\ y(x)\to \frac {\sqrt {-x^2+e^{4 c_1}}}{\sqrt {2} x} \\ y(x)\to -\frac {i}{\sqrt {2}} \\ y(x)\to \frac {i}{\sqrt {2}} \\ y(x)\to \frac {x}{\sqrt {2} \sqrt {-x^2}} \\ y(x)\to \frac {\sqrt {-x^2}}{\sqrt {2} x} \\ \end{align*}