Question

How to solve this differential equation:
x*2 dy/dx = e*y

Answer 1

separate the variables

multiply by dx, divide by x^2, divide by e^y....

Answer 2

How do I separate the variables ?

Answer 3

follow those steps

Answer 4

\[x^2 \frac{\text dy}{\text dx} = e^y\]
multiplying by \(\text dx\)
\[x^2 \text dy = e^y\text dx\]
dividing by \(x^2\)
\[ \text dy = e^yx^{-2}\text dx\]
dividing by \(e^y\)
\[ e^{-y}\text dy =x^{-2}\text dx\]

now you can integrate
\[ \int e^{-y}\text dy =\int x^{-2}\text dx\]

Answer 5

Is the answer ln x +c ?

Answer 6

\[-e^{-y}=-x^{-1}+c_1\]\[e^{-y}=x^{-1}+c\]\[\ln{e^{-y}}=\ln(x^{-1}+c)\]\[-y=\ln{(x^{-1}+c)}\]\[y=-\ln (x^{-1}+c)\]

Answer 7

I missed the minus sign. Thanks.

Answer 8

yeah you were close