Internal problem ID [7969]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 1, linear first order
Problem number: 389.
ODE order: 1.
ODE degree: 2.
CAS Maple gives this as type [_quadrature]
Solve \begin {gather*} \boxed {\left (y^{\prime }\right )^{2}-\left (4 y+1\right ) y^{\prime }+\left (4 y+1\right ) y=0} \end {gather*}
✓ Solution by Maple
Time used: 0.214 (sec). Leaf size: 193
dsolve(diff(y(x),x)^2-(4*y(x)+1)*diff(y(x),x)+(4*y(x)+1)*y(x) = 0,y(x), singsol=all)
\begin{align*} y \relax (x ) = -{\frac {1}{4}} \\ y \relax (x ) = \frac {\left (\frac {{\mathrm e}^{-2 x} c_{1} \left (\sqrt {-c_{1} {\mathrm e}^{-2 x}}-2\right )}{\sqrt {-c_{1} {\mathrm e}^{-2 x}}}-c_{1} {\mathrm e}^{-2 x}-2\right ) {\mathrm e}^{2 x}}{2 c_{1}} \\ y \relax (x ) = \frac {\left (\frac {{\mathrm e}^{-2 x} c_{1} \left (\sqrt {-c_{1} {\mathrm e}^{-2 x}}+2\right )}{\sqrt {-c_{1} {\mathrm e}^{-2 x}}}-c_{1} {\mathrm e}^{-2 x}-2\right ) {\mathrm e}^{2 x}}{2 c_{1}} \\ y \relax (x ) = -\frac {\left (-\frac {{\mathrm e}^{-2 x} c_{1} \left (\sqrt {-c_{1} {\mathrm e}^{-2 x}}+2\right )}{\sqrt {-c_{1} {\mathrm e}^{-2 x}}}+c_{1} {\mathrm e}^{-2 x}+2\right ) {\mathrm e}^{2 x}}{2 c_{1}} \\ y \relax (x ) = -\frac {\left (-\frac {{\mathrm e}^{-2 x} c_{1} \left (\sqrt {-c_{1} {\mathrm e}^{-2 x}}-2\right )}{\sqrt {-c_{1} {\mathrm e}^{-2 x}}}+c_{1} {\mathrm e}^{-2 x}+2\right ) {\mathrm e}^{2 x}}{2 c_{1}} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.235 (sec). Leaf size: 67
DSolve[y[x]*(1 + 4*y[x]) - (1 + 4*y[x])*y'[x] + y'[x]^2==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {1}{4} e^{x-4 c_1} \left (e^x+2 e^{2 c_1}\right ) \\ y(x)\to \frac {1}{4} e^{x+2 c_1} \left (-2+e^{x+2 c_1}\right ) \\ y(x)\to -\frac {1}{4} \\ y(x)\to 0 \\ \end{align*}