What is the solution for 9/10 x^2dy-18dx=0 ?

The solution for 9/10 x^2dy-18dx=0 is y=-(20)/x+c_{1}

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9/10 x^2dy-18dx=0

\frac{9}{10} x^{2} d y - 18 d x = 0

y = - \frac{20}{x} + c_{1}

Solution steps

\frac{9}{10} x^{2} d y - 18 d x = 0

Let

y

be the dependent variable. Divide by

d x

\frac{9}{10} x^{2} \frac{d y}{d x} - 18 = 0

Substitute

\frac{d y}{d x}

with

y^{'} (x)

\frac{9}{10} x^{2} y^{^{'}} (x) - 18 = 0

Isolate

y^{'} (x) : y^{'} (x) = \frac{20}{x ^{2}}

f^{^{'}} (x) = g (x)

then

f (x) = \int g (x) d x

y = \int \frac{20}{x ^{2}} d x

\int \frac{20}{x ^{2}} d x = - \frac{20}{x} + c_{1}

y = - \frac{20}{x} + c_{1}

\frac{\partial}{\partial x} (x^{3} + x^{2} y - y^{2} - 4 y)

\frac{d}{d x} (4 x + 5)

x \to 5 + lim (\frac{2}{x + 5})

\frac{\partial}{\partial x} (a x + b y^{2} + c x^{2} y)

\frac{d}{d x} (arctan (tan (x)))

What is the solution for 9/10 x^2dy-18dx=0 ?
The solution for 9/10 x^2dy-18dx=0 is y=-(20)/x+c_{1}