What is the solution for 5x^2(dy)/(dx)=(dy)/(dx)+9xe^{-y} ?

The solution for 5x^2(dy)/(dx)=(dy)/(dx)+9xe^{-y} is y=ln(9/10 ln(5x^2-1)+c_{1})

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5x^2(dy)/(dx)=(dy)/(dx)+9xe^{-y}

5 x^{2} \frac{d y}{d x} = \frac{d y}{d x} + 9 x e^{- y}

y = ln (\frac{9}{10} ln (5 x^{2} - 1) + c_{1})

Solution steps

5 x^{2} \frac{d y}{d x} = \frac{d y}{d x} + 9 x e^{- y}

Solve separable ODE:

y = ln (\frac{9}{10} ln (5 x^{2} - 1) + c_{1})

y = ln (\frac{9}{10} ln (5 x^{2} - 1) + c_{1})

\frac{d}{d x} (4 sec^{2} (4 x))

5 e^{t}

f (x) = \frac{7}{x}, at x = 3

f (x) = (x - 2)^{3} (x + 1)^{2}

\frac{d}{d x} (e^{x} cos (5 x))

What is the solution for 5x^2(dy)/(dx)=(dy)/(dx)+9xe^{-y} ?
The solution for 5x^2(dy)/(dx)=(dy)/(dx)+9xe^{-y} is y=ln(9/10 ln(5x^2-1)+c_{1})