What is the solution for (dx)/(dt)=3(x^2+1),x(pi/4)=1 ?

The solution for (dx)/(dt)=3(x^2+1),x(pi/4)=1 is x=tan(3t-pi/2)

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(dx)/(dt)=3(x^2+1),x(pi/4)=1

\frac{d x}{d t} = 3 (x^{2} + 1), x (\frac{π}{4}) = 1

x = tan (3 t - \frac{π}{2})

Solution steps

\frac{d x}{d t} = 3 (x^{2} + 1)

Solve separable ODE:

x = tan (3 t - \frac{π}{2})

x = tan (3 t - \frac{π}{2})

(1 - x^{2})^{\frac{1}{2}} y^{^{'}} = (y^{2} - 2 y + 1) arcsin (x)

\frac{d y}{d x} = 8 x y

y^{^{'}} = y^{(\frac{1}{2})}

\frac{d y}{d x} = (y x^{2})

\frac{d x}{x ^{2} y} + \frac{d y}{x y ^{2}} = 0

What is the solution for (dx)/(dt)=3(x^2+1),x(pi/4)=1 ?
The solution for (dx)/(dt)=3(x^2+1),x(pi/4)=1 is x=tan(3t-pi/2)