What is the solution for (dy)/(dx)=sin(5x),y(0)=2 ?

The solution for (dy)/(dx)=sin(5x),y(0)=2 is y=-1/5 cos(5x)+11/5

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(dy)/(dx)=sin(5x),y(0)=2

\frac{d y}{d x} = sin (5 x), y (0) = 2

y = - \frac{1}{5} cos (5 x) + \frac{11}{5}

Solution steps

\frac{d y}{d x} = sin (5 x)

Substitute

\frac{d y}{d x}

with

y^{'} (x)

y^{^{'}} (x) = sin (5 x)

f^{^{'}} (x) = g (x)

then

f (x) = \int g (x) d x

y = \int sin (5 x) d x

\int sin (5 x) d x = - \frac{1}{5} cos (5 x) + c_{1}

y = - \frac{1}{5} cos (5 x) + c_{1}

Apply initial conditions:

y = - \frac{1}{5} cos (5 x) + \frac{11}{5}

y = - \frac{1}{5} cos (5 x) + \frac{11}{5}

\frac{d ^{3}}{d x ^{3}} (x + 1)

n = 0 \sum \infty \frac{n !}{5 ^{n}}

(4, - 7), (2, - 1)

\frac{d}{d x} (8 y sin (x))

cos (x), π

What is the solution for (dy)/(dx)=sin(5x),y(0)=2 ?
The solution for (dy)/(dx)=sin(5x),y(0)=2 is y=-1/5 cos(5x)+11/5