29.15.21 problem 429

Internal problem ID [5027]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Various 15
Problem number : 429
Date solved : Monday, January 27, 2025 at 10:04:26 AM
CAS classification : [_quadrature]

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

✓ Solution by Maple

Time used: 0.001 (sec). Leaf size: 18

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

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

✓ Solution by Mathematica

Time used: 0.233 (sec). Leaf size: 61

DSolve[y[x] D[y[x],x]==Sqrt[a^2+y[x]^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 -i a \\ y(x)\to i a \\ \end{align*}