Internal problem ID [11351]
Book: An elementary treatise on differential equations by Abraham Cohen. DC heath publishers.
1906
Section: Chapter IX, Miscellaneous methods for solving equations of higher order than first.
Article 62. Summary. Page 144
Problem number: Ex 6.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type
[[_2nd_order, _missing_x], _Liouville, [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]]
\[ \boxed {y \left (1-\ln \left (y\right )\right ) y^{\prime \prime }+\left (1+\ln \left (y\right )\right ) {y^{\prime }}^{2}=0} \]
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 19
dsolve(y(x)*(1-ln(y(x)))*diff(y(x),x$2)+(1+ln(y(x)))*diff(y(x),x)^2=0,y(x), singsol=all)
\[ y \left (x \right ) = {\mathrm e}^{\frac {x c_{1} +c_{2} -1}{x c_{1} +c_{2}}} \]
✓ Solution by Mathematica
Time used: 1.021 (sec). Leaf size: 34
DSolve[y[x]*(1-Log[y[x]])*y''[x]+(1+Log[y[x]])*y'[x]^2==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to e^{\frac {c_1 x-1+c_2 c_1}{c_1 (x+c_2)}} y(x)\to e \end{align*}