What is the solution for f(x)=x^5cos(x)f^'(x) ?

The solution for f(x)=x^5cos(x)f^'(x) is f(x)=e^{integral of 1/(x^5cos(x))}

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f(x)=x^5cos(x)f^'(x)

f (x) = x^{5} cos (x) f^{^{'}} (x)

f (x) = e^{\int \frac{1}{x ^{5} c o s ( x )} d x}

Solution steps

f (x) = x^{5} cos (x) f^{'} (x)

Solve separable ODE:

f (x) = e^{\int \frac{1}{x ^{5} c o s ( x )} d x}

f (x) = e^{\int \frac{1}{x ^{5} c o s ( x )} d x}

q^{^{'}} + \frac{1}{50} q = 0.2, q (0) = 5

sin (x) sin (y) y^{^{'}} + cos (y) cos (x) = 0

3 x sin (x) d x + cos (y) d y = 0

y^{^{'}} = \frac{6 sin ( x )}{sin ( y )}, y (0) = \frac{π}{2}

y^{^{'}} = 2 x y^{2}, y (0) = \frac{1}{( 4 - x ^{2} )}

What is the solution for f(x)=x^5cos(x)f^'(x) ?
The solution for f(x)=x^5cos(x)f^'(x) is f(x)=e^{integral of 1/(x^5cos(x))}