What is the solution for y^'+9tan(9x)=7cos(9x) ?

The solution for y^'+9tan(9x)=7cos(9x) is y= 7/9 sin(9x)+ln(cos(9x))+c_{1}

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y^'+9tan(9x)=7cos(9x)

y^{^{'}} + 9 tan (9 x) = 7 cos (9 x)

y = \frac{7}{9} sin (9 x) + ln (cos (9 x)) + c_{1}

Solution steps

y^{'} (x) + 9 tan (9 x) = 7 cos (9 x)

Isolate

y^{'} (x) : y^{'} (x) = 7 cos (9 x) - 9 tan (9 x)

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

then

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

y = \int 7 cos (9 x) - 9 tan (9 x) d x

\int 7 cos (9 x) - 9 tan (9 x) d x = \frac{7}{9} sin (9 x) + ln (cos (9 x)) + c_{1}

y = \frac{7}{9} sin (9 x) + ln (cos (9 x)) + c_{1}

What is the solution for y^'+9tan(9x)=7cos(9x) ?
The solution for y^'+9tan(9x)=7cos(9x) is y= 7/9 sin(9x)+ln(cos(9x))+c_{1}