Internal problem ID [3140]
Book: Ordinary differential equations and their solutions. By George Moseley Murphy.
1960
Section: Various 14
Problem number: 394.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_separable]
Solve \begin {gather*} \boxed {y^{\prime } \sqrt {b^{2}-x^{2}}-\sqrt {a^{2}-y^{2}}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.003 (sec). Leaf size: 37
dsolve(diff(y(x),x)*sqrt(b^2-x^2) = sqrt(a^2-y(x)^2),y(x), singsol=all)
\[ \arctan \left (\frac {x}{\sqrt {b^{2}-x^{2}}}\right )-\arctan \left (\frac {y \relax (x )}{\sqrt {a^{2}-y \relax (x )^{2}}}\right )+c_{1} = 0 \]
✓ Solution by Mathematica
Time used: 4.472 (sec). Leaf size: 118
DSolve[y'[x] Sqrt[b^2-x^2]==Sqrt[a^2-y[x]^2],y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -\frac {a \tan \left (\text {ArcTan}\left (\frac {x}{\sqrt {b^2-x^2}}\right )+c_1\right )}{\sqrt {\sec ^2\left (\text {ArcTan}\left (\frac {x}{\sqrt {b^2-x^2}}\right )+c_1\right )}} \\ y(x)\to \frac {a \tan \left (\text {ArcTan}\left (\frac {x}{\sqrt {b^2-x^2}}\right )+c_1\right )}{\sqrt {\sec ^2\left (\text {ArcTan}\left (\frac {x}{\sqrt {b^2-x^2}}\right )+c_1\right )}} \\ y(x)\to -a \\ y(x)\to a \\ \end{align*}