Internal problem ID [4073]
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]
\[ \boxed {2 {y^{\prime }}^{2}+2 \left (6 y-1\right ) y^{\prime }+3 y \left (6 y-1\right )=0} \]
✓ Solution by Maple
Time used: 0.063 (sec). Leaf size: 61
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 \left (x \right ) &= {\frac {1}{6}} \\ y \left (x \right ) &= -\frac {\left (\sqrt {6}\, {\mathrm e}^{\frac {3 x}{2}+\frac {3 c_{1}}{2}}+3 \,{\mathrm e}^{3 c_{1}}\right ) {\mathrm e}^{-3 x}}{3} \\ y \left (x \right ) &= \frac {\left (\sqrt {6}\, {\mathrm e}^{\frac {3 x}{2}+\frac {3 c_{1}}{2}}-3 \,{\mathrm e}^{3 c_{1}}\right ) {\mathrm e}^{-3 x}}{3} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.275 (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*}