Internal problem ID [3647]
Book: Ordinary differential equations and their solutions. By George Moseley Murphy.
1960
Section: Various 14
Problem number: 393.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_separable]
\[ \boxed {y^{\prime } \sqrt {b^{2}+x^{2}}-\sqrt {y^{2}+a^{2}}=0} \]
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 33
dsolve(diff(y(x),x)*sqrt(b^2+x^2) = sqrt(y(x)^2+a^2),y(x), singsol=all)
\[ \ln \left (x +\sqrt {b^{2}+x^{2}}\right )-\ln \left (y \left (x \right )+\sqrt {y \left (x \right )^{2}+a^{2}}\right )+c_{1} = 0 \]
✓ Solution by Mathematica
Time used: 11.551 (sec). Leaf size: 167
DSolve[y'[x] Sqrt[x^2+b^2]==Sqrt[y[x]^2+a^2],y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -\frac {e^{-c_1} \sqrt {a^2 \left (2 x \left (\left (-1+e^{4 c_1}\right ) \sqrt {b^2+x^2}+\left (1+e^{4 c_1}\right ) x\right )+b^2 \left (-1+e^{2 c_1}\right ){}^2\right )}}{2 b} y(x)\to \frac {e^{-c_1} \sqrt {a^2 \left (2 x \left (\left (-1+e^{4 c_1}\right ) \sqrt {b^2+x^2}+\left (1+e^{4 c_1}\right ) x\right )+b^2 \left (-1+e^{2 c_1}\right ){}^2\right )}}{2 b} y(x)\to -i a y(x)\to i a \end{align*}