What is the solution for (dy)/(dx)=2cos(x)(y+1),y(pi/6)=2 ?

The solution for (dy)/(dx)=2cos(x)(y+1),y(pi/6)=2 is y=3e^{2sin(x)-1}-1

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(dy)/(dx)=2cos(x)(y+1),y(pi/6)=2

\frac{d y}{d x} = 2 cos (x) (y + 1), y (\frac{π}{6}) = 2

y = 3 e^{2 s i n (x) - 1} - 1

Solution steps

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

Solve separable ODE:

y = 3 e^{2 s i n (x) - 1} - 1

y = 3 e^{2 s i n (x) - 1} - 1

\frac{\partial}{\partial x} (2 x^{2} y^{2})

n = 0 \sum \infty 9 (\frac{3}{4})^{n}

\int - 2 y d y

\frac{1}{2 y ^{\frac{3}{2}}}

\int_{0}^{1} \frac{1}{4 x - 1} d x

What is the solution for (dy)/(dx)=2cos(x)(y+1),y(pi/6)=2 ?
The solution for (dy)/(dx)=2cos(x)(y+1),y(pi/6)=2 is y=3e^{2sin(x)-1}-1