What is the solution for (dy)/(dx)=cos(x)(1+3y) ?

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

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(dy)/(dx)=cos(x)(1+3y)

\frac{d y}{d x} = cos (x) (1 + 3 y)

y = \frac{e ^{3 s i n (x) + c_{1}}}{3} - \frac{1}{3}

Solution steps

\frac{d y}{d x} = cos (x) (1 + 3 y)

Solve separable ODE:

y = \frac{e ^{3 s i n (x) + c_{1}}}{3} - \frac{1}{3}

y = \frac{e ^{3 s i n (x) + c_{1}}}{3} - \frac{1}{3}

\frac{\partial}{\partial x} (x^{6} y^{6} + 4 x^{6} y)

\frac{\partial}{\partial x} (x \cdot e^{- x^{2} - y^{2}})

\int x 2 - x^{2} d x

\frac{x ^{2} d y}{d x} = y - x y, y [- 1] = - 4

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

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