Internal problem ID [4153]
Book: Ordinary differential equations and their solutions. By George Moseley Murphy.
1960
Section: Various 31
Problem number: 917.
ODE order: 1.
ODE degree: 2.
CAS Maple gives this as type [_quadrature]
\[ \boxed {\left (a^{2}-x^{2}\right ) {y^{\prime }}^{2}=-b^{2}} \]
✓ Solution by Maple
Time used: 0.078 (sec). Leaf size: 44
dsolve((a^2-x^2)*diff(y(x),x)^2+b^2 = 0,y(x), singsol=all)
\begin{align*} y \left (x \right ) &= b \ln \left (x +\sqrt {-a^{2}+x^{2}}\right )+c_{1} \\ y \left (x \right ) &= -b \ln \left (x +\sqrt {-a^{2}+x^{2}}\right )+c_{1} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.007 (sec). Leaf size: 109
DSolve[(a^2-x^2) (y'[x])^2+b^2==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {1}{2} b \log \left (1-\frac {x}{\sqrt {x^2-a^2}}\right )-\frac {1}{2} b \log \left (\frac {x}{\sqrt {x^2-a^2}}+1\right )+c_1 \\ y(x)\to -\frac {1}{2} b \log \left (1-\frac {x}{\sqrt {x^2-a^2}}\right )+\frac {1}{2} b \log \left (\frac {x}{\sqrt {x^2-a^2}}+1\right )+c_1 \\ \end{align*}