29.19.27 problem 540

Internal problem ID [5136]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Various 19
Problem number : 540
Date solved : Monday, January 27, 2025 at 10:13:50 AM
CAS classification : [_separable]

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

✓ Solution by Maple

Time used: 0.006 (sec). Leaf size: 36

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

\begin{align*} y \left (x \right ) &= \frac {\sqrt {\left (-a x +c_{1} \right ) x}}{x} \\ y \left (x \right ) &= -\frac {\sqrt {\left (-a x +c_{1} \right ) x}}{x} \\ \end{align*}

✓ Solution by Mathematica

Time used: 0.348 (sec). Leaf size: 115

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

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