Internal problem ID [4152]
Book: Ordinary differential equations and their solutions. By George Moseley Murphy.
1960
Section: Various 31
Problem number: 916.
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: 0.031 (sec). Leaf size: 40
dsolve((a^2+x^2)*diff(y(x),x)^2 = b^2,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: 0.005 (sec). Leaf size: 101
DSolve[(a^2+x^2) (y'[x])^2==b^2,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {1}{2} b \log \left (1-\frac {x}{\sqrt {a^2+x^2}}\right )-\frac {1}{2} b \log \left (\frac {x}{\sqrt {a^2+x^2}}+1\right )+c_1 y(x)\to -\frac {1}{2} b \log \left (1-\frac {x}{\sqrt {a^2+x^2}}\right )+\frac {1}{2} b \log \left (\frac {x}{\sqrt {a^2+x^2}}+1\right )+c_1 \end{align*}