Internal problem ID [8725]
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]
\[ \boxed {{y^{\prime }}^{2}-\left (1+4 y\right ) y^{\prime }+\left (1+4 y\right ) y=0} \]
✓ Solution by Maple
Time used: 0.062 (sec). Leaf size: 137
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 \left (x \right ) &= -{\frac {1}{4}} \\ y \left (x \right ) &= -\frac {\sqrt {-{\mathrm e}^{-2 x} c_{1}}\, {\mathrm e}^{2 x}+c_{1}}{c_{1} \sqrt {-{\mathrm e}^{-2 x} c_{1}}} \\ y \left (x \right ) &= \frac {-\sqrt {-{\mathrm e}^{-2 x} c_{1}}\, {\mathrm e}^{2 x}+c_{1}}{\sqrt {-{\mathrm e}^{-2 x} c_{1}}\, c_{1}} \\ y \left (x \right ) &= \frac {-\sqrt {-{\mathrm e}^{-2 x} c_{1}}\, {\mathrm e}^{2 x}+c_{1}}{\sqrt {-{\mathrm e}^{-2 x} c_{1}}\, c_{1}} \\ y \left (x \right ) &= -\frac {\sqrt {-{\mathrm e}^{-2 x} c_{1}}\, {\mathrm e}^{2 x}+c_{1}}{c_{1} \sqrt {-{\mathrm e}^{-2 x} c_{1}}} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.208 (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*}