What is the solution for 4/10 x^2dy-13dx=0 ?

The solution for 4/10 x^2dy-13dx=0 is y=-(65)/(2x)+c_{1}

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4/10 x^2dy-13dx=0

\frac{4}{10} x^{2} d y - 13 d x = 0

y = - \frac{65}{2 x} + c_{1}

Solution steps

\frac{4}{10} x^{2} d y - 13 d x = 0

Let

y

be the dependent variable. Divide by

d x

\frac{4}{10} x^{2} \frac{d y}{d x} - 13 = 0

Substitute

\frac{d y}{d x}

with

y^{'} (x)

\frac{4}{10} x^{2} y^{^{'}} (x) - 13 = 0

Isolate

y^{'} (x) : y^{'} (x) = \frac{65}{2 x ^{2}}

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

then

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

y = \int \frac{65}{2 x ^{2}} d x

\int \frac{65}{2 x ^{2}} d x = - \frac{65}{2 x} + c_{1}

y = - \frac{65}{2 x} + c_{1}

What is the solution for 4/10 x^2dy-13dx=0 ?
The solution for 4/10 x^2dy-13dx=0 is y=-(65)/(2x)+c_{1}