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})

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

\frac{\partial}{\partial x} (\frac{x}{1 + x ^{2}})

y (x + 4) = 1, x = 0, y = 0, x = 4

\int (ln (16 x))^{2} d x

\int (- 6 x^{6} - 2 x^{3} - 4) d x

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)