29.15.22 problem 430

Internal problem ID [5028]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Various 15
Problem number : 430
Date solved : Monday, January 27, 2025 at 10:04:33 AM
CAS classification : [_quadrature]

\begin{align*} y^{\prime } y&=\sqrt {y^{2}-a^{2}} \end{align*}

✓ Solution by Maple

Time used: 0.002 (sec). Leaf size: 29

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

\[ x +\frac {\left (-y \left (x \right )+a \right ) \left (y \left (x \right )+a \right )}{\sqrt {y \left (x \right )^{2}-a^{2}}}+c_{1} = 0 \]

✓ Solution by Mathematica

Time used: 0.237 (sec). Leaf size: 51

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

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