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

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

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

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

x = tan (4 t + \frac{π}{4} - π)

Solution steps

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

Solve separable ODE:

x = tan (4 t + \frac{π}{4} - π)

x = tan (4 t + \frac{π}{4} - π)

\int tan^{4} (2 x) d x

t^{5} y^{4} - t^{3} y^{^{'}} + 6 y = 0

y^{^{'}} = \frac{3 ( e ^{x} + 1 )}{2 y}

\frac{d}{dd} (\frac{a x + b}{c x + d})

\frac{d}{d x} (- \frac{1}{2} x^{4} cos (x))

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