29.14.12 problem 393

Internal problem ID [4991]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Various 14
Problem number : 393
Date solved : Monday, January 27, 2025 at 10:01:31 AM
CAS classification : [_separable]

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

✓ Solution by Maple

Time used: 0.002 (sec). Leaf size: 33

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

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

✓ Solution by Mathematica

Time used: 0.384 (sec). Leaf size: 76

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

\begin{align*} y(x)\to \frac {a^2 e^{-c_1} \left (x-\sqrt {b^2+x^2}\right )}{2 b^2}+\frac {1}{2} e^{c_1} \left (\sqrt {b^2+x^2}+x\right ) \\ y(x)\to -i a \\ y(x)\to i a \\ \end{align*}