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

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

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

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

y = tan (4 x + c_{1})

Solution steps

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

Solve separable ODE:

y = tan (4 x + c_{1})

y = tan (4 x + c_{1})

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

\frac{d x}{d t} = - \frac{x}{50 π}

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

x^{2} \frac{d y}{d x} + x y = 3 x

y^{^{'}} = \frac{5 sin ( x )}{sin ( y )}, y (0) = \frac{π}{2}

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