What is the solution for (dy)/(dx)(sqrt(25-x^2))+5xy=0 ?

The solution for (dy)/(dx)(sqrt(25-x^2))+5xy=0 is y=e^{5sqrt(25-x^2)+c_{1}}

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(dy)/(dx)(sqrt(25-x^2))+5xy=0

\frac{d y}{d x} (25 - x^{2}) + 5 x y = 0

y = e^{5 25 - x^{2} + c_{1}}

Solution steps

\frac{d y}{d x} (25 - x^{2}) + 5 x y = 0

Solve separable ODE:

y = e^{5 25 - x^{2} + c_{1}}

y = e^{5 25 - x^{2} + c_{1}}

\frac{d}{d x} (\frac{( 1 - x ) ^{2}}{x ^{2}})

y^{^{'}} = y x e^{x^{2}} - y

x \to 0 - lim (x^{2} ln (x))

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

\frac{d}{d x} (\frac{x ^{2}}{10 + x})

What is the solution for (dy)/(dx)(sqrt(25-x^2))+5xy=0 ?
The solution for (dy)/(dx)(sqrt(25-x^2))+5xy=0 is y=e^{5sqrt(25-x^2)+c_{1}}