What is the solution for (dy)/(dx)=x^5(y-5),y(0)=8 ?

The solution for (dy)/(dx)=x^5(y-5),y(0)=8 is y=3e^{(x^6)/6}+5

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(dy)/(dx)=x^5(y-5),y(0)=8

\frac{d y}{d x} = x^{5} (y - 5), y (0) = 8

y = 3 e^{\frac{x ^{6}}{6}} + 5

Solution steps

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

Solve separable ODE:

y = 3 e^{\frac{x ^{6}}{6}} + 5

y = 3 e^{\frac{x ^{6}}{6}} + 5

(1 - x^{2}) y^{^{'}} - y^{2} = 0

\frac{d x}{d t} = 125 - \frac{x}{100}, x (0) = 4000

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

\frac{d x}{d t} = t \cdot x^{\frac{1}{2}}

\frac{d y}{d x} = \frac{cos ^{2} ( y )}{4 x - 3}

What is the solution for (dy)/(dx)=x^5(y-5),y(0)=8 ?
The solution for (dy)/(dx)=x^5(y-5),y(0)=8 is y=3e^{(x^6)/6}+5