Internal problem ID [3565]
Book: Ordinary differential equations and their solutions. By George Moseley Murphy.
1960
Section: Various 29
Problem number: 834.
ODE order: 1.
ODE degree: 2.
CAS Maple gives this as type [_quadrature]
Solve \begin {gather*} \boxed {2 \left (y^{\prime }\right )^{2}+2 \left (6 y-1\right ) y^{\prime }+3 y \left (6 y-1\right )=0} \end {gather*}
✓ Solution by Maple
Time used: 3.969 (sec). Leaf size: 204
dsolve(2*diff(y(x),x)^2+2*(6*y(x)-1)*diff(y(x),x)+3*y(x)*(6*y(x)-1) = 0,y(x), singsol=all)
\begin{align*} y \relax (x ) = {\frac {1}{6}} \\ y \relax (x ) = -\frac {{\mathrm e}^{-3 x} {\mathrm e}^{3 c_{1}} \left (\sqrt {6}\, {\mathrm e}^{-\frac {3 x}{2}} {\mathrm e}^{\frac {3 c_{1}}{2}}-3 \,{\mathrm e}^{-3 x} {\mathrm e}^{3 c_{1}}\right )}{3 \,{\mathrm e}^{-3 x} {\mathrm e}^{3 c_{1}}-2}-2 \,{\mathrm e}^{-3 x} {\mathrm e}^{3 c_{1}}+\frac {\frac {2 \sqrt {6}\, {\mathrm e}^{-\frac {3 x}{2}} {\mathrm e}^{\frac {3 c_{1}}{2}}}{3}-2 \,{\mathrm e}^{-3 x} {\mathrm e}^{3 c_{1}}}{3 \,{\mathrm e}^{-3 x} {\mathrm e}^{3 c_{1}}-2} \\ y \relax (x ) = \frac {{\mathrm e}^{-3 x} {\mathrm e}^{3 c_{1}} \left (\sqrt {6}\, {\mathrm e}^{-\frac {3 x}{2}} {\mathrm e}^{\frac {3 c_{1}}{2}}+3 \,{\mathrm e}^{-3 x} {\mathrm e}^{3 c_{1}}\right )}{3 \,{\mathrm e}^{-3 x} {\mathrm e}^{3 c_{1}}-2}-2 \,{\mathrm e}^{-3 x} {\mathrm e}^{3 c_{1}}-\frac {2 \left (\sqrt {6}\, {\mathrm e}^{-\frac {3 x}{2}} {\mathrm e}^{\frac {3 c_{1}}{2}}+3 \,{\mathrm e}^{-3 x} {\mathrm e}^{3 c_{1}}\right )}{3 \left (3 \,{\mathrm e}^{-3 x} {\mathrm e}^{3 c_{1}}-2\right )} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.257 (sec). Leaf size: 81
DSolve[2 (y'[x])^2+2(6 y[x]-1)y'[x]+3 y[x](6 y[x]-1)==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -\frac {1}{6} e^{-3 x+3 c_1} \left (2 e^{3 x/2}+e^{3 c_1}\right ) \\ y(x)\to \frac {1}{6} e^{-3 (x+2 c_1)} \left (-1+2 e^{\frac {3 x}{2}+3 c_1}\right ) \\ y(x)\to 0 \\ y(x)\to \frac {1}{6} \\ \end{align*}