Internal problem ID [5438]
Book: Schaums Outline. Theory and problems of Differential Equations, 1st edition. Frank Ayres.
McGraw Hill 1952
Section: Chapter 19. Linear equations with variable coefficients (Misc. types). Supplemetary
problems. Page 132
Problem number: 31.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_xy]]
\[ \boxed {y y^{\prime \prime }-{y^{\prime }}^{2}-y^{2} \ln \left (y\right )=0} \]
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 21
dsolve(y(x)*diff(y(x),x$2)-diff(y(x),x)^2=y(x)^2*ln(y(x)),y(x), singsol=all)
\[ y = {\mathrm e}^{\frac {{\mathrm e}^{-2 x} c_{1} {\mathrm e}^{x}}{2}} {\mathrm e}^{-\frac {c_{2} {\mathrm e}^{x}}{2}} \]
✓ Solution by Mathematica
Time used: 2.66 (sec). Leaf size: 73
DSolve[y[x]*y''[x]-y'[x]^2==y[x]^2*Log[y[x]],y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \exp \left (-\frac {1}{2} \sqrt {c_1} e^{-x-c_2} \left (-1+e^{2 (x+c_2)}\right )\right ) y(x)\to \exp \left (\frac {1}{2} \sqrt {c_1} e^{-x-c_2} \left (-1+e^{2 (x+c_2)}\right )\right ) \end{align*}