What is the solution for (dy)/(dx)=50y-1/10 y^2 ?

The solution for (dy)/(dx)=50y-1/10 y^2 is y=-(500e^{50x+50c_{1}})/(1-e^{50(x+c_{1))}}

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(dy)/(dx)=50y-1/10 y^2

\frac{d y}{d x} = 50 y - \frac{1}{10} y^{2}

y = - \frac{500 e ^{50 x + 50 c_{1}}}{1 - e ^{50 (x + c_{1})}}

Solution steps

\frac{d y}{d x} = 50 y - \frac{1}{10} y^{2}

Solve separable ODE:

y = - \frac{500 e ^{50 x + 50 c_{1}}}{1 - e ^{50 (x + c_{1})}}

y = - \frac{500 e ^{50 x + 50 c_{1}}}{1 - e ^{50 (x + c_{1})}}

x^{2} + 1

\int (\frac{1}{5 x ^{3.3}}) d x

\int \frac{12}{( 36 x ^{2} + 1 ) ^{2}} d x

ln (3 x^{2})

h (x) = 3 e^{x} - 7 x, (0, 3)

What is the solution for (dy)/(dx)=50y-1/10 y^2 ?
The solution for (dy)/(dx)=50y-1/10 y^2 is y=-(500e^{50x+50c_{1}})/(1-e^{50(x+c_{1))}}