What is the solution for (dy)/(dx)=sin(3x)-cos(5x) ?

The solution for (dy)/(dx)=sin(3x)-cos(5x) is y=-1/3 cos(3x)-1/5 sin(5x)+c_{1}

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(dy)/(dx)=sin(3x)-cos(5x)

\frac{d y}{d x} = sin (3 x) - cos (5 x)

y = - \frac{1}{3} cos (3 x) - \frac{1}{5} sin (5 x) + c_{1}

Solution steps

\frac{d y}{d x} = sin (3 x) - cos (5 x)

Substitute

\frac{d y}{d x}

with

y^{'} (x)

y^{^{'}} (x) = sin (3 x) - cos (5 x)

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

then

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

y = \int sin (3 x) - cos (5 x) d x

\int sin (3 x) - cos (5 x) d x = - \frac{1}{3} cos (3 x) - \frac{1}{5} sin (5 x) + c_{1}

y = - \frac{1}{3} cos (3 x) - \frac{1}{5} sin (5 x) + c_{1}

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What is the solution for (dy)/(dx)=sin(3x)-cos(5x) ?
The solution for (dy)/(dx)=sin(3x)-cos(5x) is y=-1/3 cos(3x)-1/5 sin(5x)+c_{1}