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 = 0.0499261 (sec), leaf count = 55
\[\left \{\left \{y(x)\to \frac {1}{4} e^{x-4 c_1} \left (e^x-2 e^{2 c_1}\right )\right \},\left \{y(x)\to \frac {1}{4} e^{2 c_1+x} \left (e^{2 c_1+x}-2\right )\right \}\right \}\]
Maple ✓
cpu = 0.048 (sec), leaf count = 49
\[ \left \{ x-{\frac {\ln \left ( y \left ( x \right ) \right ) }{2}}-{\it Artanh} \left ( \sqrt {1+4\,y \left ( x \right ) } \right ) -{\it \_C1}=0,x-{\frac {\ln \left ( y \left ( x \right ) \right ) }{2}}+{\it Artanh} \left ( \sqrt {1+4\,y \left ( x \right ) } \right ) -{\it \_C1}=0,y \left ( x \right ) =-{\frac {1}{4}} \right \} \] 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),'implicit')
Maple raw output
y(x) = -1/4, x-1/2*ln(y(x))+arctanh((1+4*y(x))^(1/2))-_C1 = 0, x-1/2*ln(y(x))-arctanh((1+4*y(x))^(1/2))-_C1 = 0