ODE
\[ y'(x)^2-(4 y(x)+1) y'(x)+y(x) (4 y(x)+1)=0 \] ODE Classification
[_quadrature]
Book solution method
Missing Variables ODE, Independent variable missing, Solve for \(y'\)
Mathematica ✓
cpu = 0.238281 (sec), leaf count = 55
\[\left \{\left \{y(x)\to \frac {1}{4} e^{x-4 c_1} \left (e^x-2 e^{2 c_1}\right )\right \},\left \{y(x)\to \frac {1}{4} e^{x+2 c_1} \left (-2+e^{x+2 c_1}\right )\right \}\right \}\]
Maple ✓
cpu = 4.193 (sec), leaf count = 193
\[\left [y \left (x \right ) = -{\frac {1}{4}}, y \left (x \right ) = \frac {\left (\frac {{\mathrm e}^{-2 x} \textit {\_C1} \left (\sqrt {-{\mathrm e}^{-2 x} \textit {\_C1}}-2\right )}{\sqrt {-{\mathrm e}^{-2 x} \textit {\_C1}}}-{\mathrm e}^{-2 x} \textit {\_C1} -2\right ) {\mathrm e}^{2 x}}{2 \textit {\_C1}}, y \left (x \right ) = \frac {\left (\frac {{\mathrm e}^{-2 x} \textit {\_C1} \left (\sqrt {-{\mathrm e}^{-2 x} \textit {\_C1}}+2\right )}{\sqrt {-{\mathrm e}^{-2 x} \textit {\_C1}}}-{\mathrm e}^{-2 x} \textit {\_C1} -2\right ) {\mathrm e}^{2 x}}{2 \textit {\_C1}}, y \left (x \right ) = -\frac {\left (-\frac {{\mathrm e}^{-2 x} \textit {\_C1} \left (\sqrt {-{\mathrm e}^{-2 x} \textit {\_C1}}+2\right )}{\sqrt {-{\mathrm e}^{-2 x} \textit {\_C1}}}+{\mathrm e}^{-2 x} \textit {\_C1} +2\right ) {\mathrm e}^{2 x}}{2 \textit {\_C1}}, y \left (x \right ) = -\frac {\left (-\frac {{\mathrm e}^{-2 x} \textit {\_C1} \left (\sqrt {-{\mathrm e}^{-2 x} \textit {\_C1}}-2\right )}{\sqrt {-{\mathrm e}^{-2 x} \textit {\_C1}}}+{\mathrm e}^{-2 x} \textit {\_C1} +2\right ) {\mathrm e}^{2 x}}{2 \textit {\_C1}}\right ]\] Mathematica raw input
DSolve[y[x]*(1 + 4*y[x]) - (1 + 4*y[x])*y'[x] + y'[x]^2 == 0,y[x],x]
Mathematica raw output
{{y[x] -> (E^(x - 4*C[1])*(E^x - 2*E^(2*C[1])))/4}, {y[x] -> (E^(x + 2*C[1])*(-2 + E^(x + 2*C[1])))/4}}
Maple raw input
dsolve(diff(y(x),x)^2-(1+4*y(x))*diff(y(x),x)+(1+4*y(x))*y(x) = 0, y(x))
Maple raw output
[y(x) = -1/4, y(x) = 1/2*(1/exp(x)^2*_C1*((-1/exp(x)^2*_C1)^(1/2)-2)/(-1/exp(x)^2*_C1)^(1/2)-1/exp(x)^2*_C1-2)*exp(x)^2/_C1, y(x) = 1/2*(1/exp(x)^2*_C1*((-1/exp(x)^2*_C1)^(1/2)+2)/(-1/exp(x)^2*_C1)^(1/2)-1/exp(x)^2*_C1-2)*exp(x)^2/_C1, y(x) = -1/2*(-1/exp(x)^2*_C1*((-1/exp(x)^2*_C1)^(1/2)+2)/(-1/exp(x)^2*_C1)^(1/2)+1/exp(x)^2*_C1+2)*exp(x)^2/_C1, y(x) = -1/2*(-1/exp(x)^2*_C1*((-1/exp(x)^2*_C1)^(1/2)-2)/(-1/exp(x)^2*_C1)^(1/2)+1/exp(x)^2*_C1+2)*exp(x)^2/_C1]