What is the solution for y^'tan(x)=9a+y,y(pi/3)=9a ?

The solution for y^'tan(x)=9a+y,y(pi/3)=9a is y=12asin(x)*3^{1/2}-9a

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y^'tan(x)=9a+y,y(pi/3)=9a

y^{^{'}} tan (x) = 9 a + y, y (\frac{π}{3}) = 9 a

y = 12 a sin (x) \cdot 3^{\frac{1}{2}} - 9 a

Solution steps

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

Solve separable ODE:

y = 12 a sin (x) \cdot 3^{\frac{1}{2}} - 9 a

y = 12 a sin (x) \cdot 3^{\frac{1}{2}} - 9 a

x^{5} \cdot y^{^{'}} + y^{5} = 0

\frac{d x}{1 + x ^{2}} + \frac{d y}{1 + y ^{2}} = 0

x cos (y) \frac{d y}{d x} - sin (y) = 0

x^{(- 2)} y^{(- 5)} d x + x^{(- 3)} y^{(- 4)} d y = 0

y^{^{'}} + x - x^{2} \cdot y = x - x^{2}

What is the solution for y^'tan(x)=9a+y,y(pi/3)=9a ?
The solution for y^'tan(x)=9a+y,y(pi/3)=9a is y=12asin(x)*3^{1/2}-9a