Internal problem ID [4005]
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]
\[ \boxed {{y^{\prime }}^{2}-a^{2} \left (1-\ln \left (y\right )^{2}\right ) y^{2}=0} \]
✓ Solution by Maple
Time used: 0.047 (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 \left (x \right ) = {\mathrm e}^{\operatorname {RootOf}\left (a^{2} {\mathrm e}^{2 \textit {\_Z}} \left (\textit {\_Z}^{2}-1\right )\right )} y \left (x \right ) = {\mathrm e}^{-\sin \left (\left (c_{1} -x \right ) a \right )} y \left (x \right ) = {\mathrm e}^{\sin \left (c_{1} a -a x \right )} \end{align*}
✓ Solution by Mathematica
Time used: 16.422 (sec). Leaf size: 197
DSolve[(y'[x])^2==a^2(1-Log[y[x]]^2)y[x]^2,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \exp \left (-\frac {1}{2} \sqrt {-e^{2 i a x-2 c_1}-e^{2 c_1-2 i a x}+2}\right ) y(x)\to \exp \left (\frac {1}{2} \sqrt {-e^{2 i a x-2 c_1}-e^{2 c_1-2 i a x}+2}\right ) y(x)\to \exp \left (-\frac {1}{2} \sqrt {-e^{-2 i a x-2 c_1} \left (-1+e^{2 i a x+2 c_1}\right ){}^2}\right ) y(x)\to \exp \left (\frac {1}{2} \sqrt {-e^{-2 i a x-2 c_1} \left (-1+e^{2 i a x+2 c_1}\right ){}^2}\right ) y(x)\to \frac {1}{e} y(x)\to e \end{align*}