Internal problem ID [3497]
Book: Ordinary differential equations and their solutions. By George Moseley Murphy.
1960
Section: Various 26
Problem number: 764.
ODE order: 1.
ODE degree: 2.
CAS Maple gives this as type [_quadrature]
Solve \begin {gather*} \boxed {\left (y^{\prime }\right )^{2}-a^{2} \left (1-\ln \relax (y)^{2}\right ) y^{2}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.094 (sec). Leaf size: 47
dsolve(diff(y(x),x)^2 = a^2*(1-ln(y(x))^2)*y(x)^2,y(x), singsol=all)
\begin{align*} y \relax (x ) = {\mathrm e}^{\RootOf \left (a^{2} {\mathrm e}^{2 \textit {\_Z}} \left (\textit {\_Z}^{2}-1\right )\right )} \\ y \relax (x ) = {\mathrm e}^{-\sin \left (-a x +c_{1} a \right )} \\ y \relax (x ) = {\mathrm e}^{\sin \left (-a x +c_{1} a \right )} \\ \end{align*}
✓ Solution by Mathematica
Time used: 11.53 (sec). Leaf size: 157
DSolve[(y'[x])^2==a^2(1-Log[y[x]]^2)y[x]^2,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {1}{\cosh (\sin (a x+i c_1))+\sinh \left (\sqrt {\sin ^2(a x+i c_1)}\right )} \\ y(x)\to \cosh (\sin (a x+i c_1))+\sinh \left (\sqrt {\sin ^2(a x+i c_1)}\right ) \\ y(x)\to \cosh (\sin (a x-i c_1))-\sinh \left (\sqrt {\sin ^2(a x-i c_1)}\right ) \\ y(x)\to \cosh (\sin (a x-i c_1))+\sinh \left (\sqrt {\sin ^2(a x-i c_1)}\right ) \\ y(x)\to \frac {1}{e} \\ y(x)\to e \\ \end{align*}