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

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

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

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

x = tan (2 t - \frac{π}{4})

Solution steps

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

Solve separable ODE:

x = tan (2 t - \frac{π}{4})

x = tan (2 t - \frac{π}{4})

\int \frac{x ^{2} - 2 x - 1}{x} d x

e^{1 - t}

x y^{^{'}} sin^{2} (\frac{y}{x}) = x + y sin^{2} (\frac{y}{x})

\frac{\partial}{\partial x} (8 y^{7} cos (8 x))

\frac{1}{b ^{\frac{2}{7}}}

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