31.19 problem 918

Internal problem ID [3646]

Book: Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section: Various 31
Problem number: 918.
ODE order: 1.
ODE degree: 2.

CAS Maple gives this as type [_quadrature]

Solve \begin {gather*} \boxed {\left (a^{2}-x^{2}\right ) \left (y^{\prime }\right )^{2}-b^{2}=0} \end {gather*}

Solution by Maple

Time used: 0.096 (sec). Leaf size: 44

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

\begin{align*} y \relax (x ) = b \arctan \left (\frac {x}{\sqrt {a^{2}-x^{2}}}\right )+c_{1} \\ y \relax (x ) = -b \arctan \left (\frac {x}{\sqrt {a^{2}-x^{2}}}\right )+c_{1} \\ \end{align*}

Solution by Mathematica

Time used: 0.009 (sec). Leaf size: 52

DSolve[(a^2-x^2) (y'[x])^2==b^2,y[x],x,IncludeSingularSolutions -> True]
 

\begin{align*} y(x)\to -b \text {ArcTan}\left (\frac {x}{\sqrt {a^2-x^2}}\right )+c_1 \\ y(x)\to b \text {ArcTan}\left (\frac {x}{\sqrt {a^2-x^2}}\right )+c_1 \\ \end{align*}