What is the solution for (y)^6(((dy)/(dx)-5)/3)=tan(3x)-5/3 (y)^6 ?

The solution for (y)^6(((dy)/(dx)-5)/3)=tan(3x)-5/3 (y)^6 is y=\sqrt[7]{-7ln(cos(3x))+c_{1}}

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(y)^6(((dy)/(dx)-5)/3)=tan(3x)-5/3 (y)^6

(y)^{6} (\frac{\frac{d y}{d x} - 5}{3}) = tan (3 x) - \frac{5}{3} (y)^{6}

y = 7 - 7 ln (cos (3 x)) + c_{1}

Solution steps

(y)^{6} (\frac{\frac{d y}{d x} - 5}{3}) = tan (3 x) - \frac{5}{3} (y)^{6}

Solve separable ODE:

y = 7 - 7 ln (cos (3 x)) + c_{1}

y = 7 - 7 ln (cos (3 x)) + c_{1}

\frac{d p}{d t} = 3 p - p^{2}

\frac{d y}{d x} = \frac{ln ( x ^{6} )}{x y ^{2}}, y (1) = 5

y - 2 y^{^{'}} = 5

y^{^{'}} = \frac{7 x ^{2} - 1}{7 + 8 y}

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

What is the solution for (y)^6(((dy)/(dx)-5)/3)=tan(3x)-5/3 (y)^6 ?
The solution for (y)^6(((dy)/(dx)-5)/3)=tan(3x)-5/3 (y)^6 is y=\sqrt[7]{-7ln(cos(3x))+c_{1}}