What is the solution for (dy)/(dx)=15sin(pi/(20)(x-2))+2 ?

The solution for (dy)/(dx)=15sin(pi/(20)(x-2))+2 is y=-(300)/pi cos((pi(x-2))/(20))+2(x-2)+c_{1}

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(dy)/(dx)=15sin(pi/(20)(x-2))+2

\frac{d y}{d x} = 15 sin (\frac{π}{20} (x - 2)) + 2

y = - \frac{300}{π} cos (\frac{π ( x - 2 )}{20}) + 2 (x - 2) + c_{1}

Solution steps

\frac{d y}{d x} = 15 sin (\frac{π}{20} (x - 2)) + 2

Substitute

\frac{d y}{d x}

with

y^{'} (x)

y^{^{'}} (x) = 15 sin (\frac{π}{20} (x - 2)) + 2

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

then

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

y = \int 15 sin (\frac{π}{20} (x - 2)) + 2 d x

\int 15 sin (\frac{π}{20} (x - 2)) + 2 d x = - \frac{300}{π} cos (\frac{π ( x - 2 )}{20}) + 2 (x - 2) + c_{1}

y = - \frac{300}{π} cos (\frac{π ( x - 2 )}{20}) + 2 (x - 2) + c_{1}

y = tan (18 x^{2}), at x = π

\int 2 cos (7 x - 4) d x

y^{^{''}} + 9 y = csc^{2} (3 t)

y^{^{'}} = 2 y - t^{2}

\int_{0}^{2} sin (x^{2}) d x

What is the solution for (dy)/(dx)=15sin(pi/(20)(x-2))+2 ?
The solution for (dy)/(dx)=15sin(pi/(20)(x-2))+2 is y=-(300)/pi cos((pi(x-2))/(20))+2(x-2)+c_{1}