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

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

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

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

x = tan (4 y + \frac{π}{4} - π)

Solution steps

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

Solve separable ODE:

x = tan (4 y + \frac{π}{4} - π)

x = tan (4 y + \frac{π}{4} - π)

t (\frac{d y}{d t}) = t^{3} + 22 t^{3} y

\int (1 + cos (θ))^{2} d θ

y = \frac{1}{x}, y = x, y = \frac{1}{4} x

\int_{1}^{6} \frac{x ^{2} + 5}{7 x - x ^{2}} d x

\frac{cos ( 7 t )}{e ^{5 t}}

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