What is the solution for (dx)/(dt)=8(x^2+1),x(pi/4)=1 ?

The solution for (dx)/(dt)=8(x^2+1),x(pi/4)=1 is x=tan(8t+pi/4-2pi)

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(dx)/(dt)=8(x^2+1),x(pi/4)=1

\frac{d x}{d t} = 8 (x^{2} + 1), x (\frac{π}{4}) = 1

x = tan (8 t + \frac{π}{4} - 2 π)

Solution steps

\frac{d x}{d t} = 8 (x^{2} + 1)

Solve separable ODE:

x = tan (8 t + \frac{π}{4} - 2 π)

x = tan (8 t + \frac{π}{4} - 2 π)

\frac{d}{d x} (\frac{- 1}{( x - 1 ) ^{2}})

\frac{d y}{d t} - 2 t y = 12 t^{2} e^{t^{2}}

y^{^{'}} = (2 y^{2}) + x y^{2}

f^{^{'}} (x) = 2 x - \frac{3}{x ^{4}}

f (x) = \frac{2}{3 x + 1}

What is the solution for (dx)/(dt)=8(x^2+1),x(pi/4)=1 ?
The solution for (dx)/(dt)=8(x^2+1),x(pi/4)=1 is x=tan(8t+pi/4-2pi)