How Do You Solve This Differential Equation: \( x^3 \frac{dy}{dx} = y \)?

[seto6]

Homework Statement

hey, it's been on my wish list for some time, i have decided to teach my self diffrential equal, rather than waiting to be taught at school, after having some exposure through vibrations and circuits.

so i got a book and i started to learn, the question came to be;

$$x^{3}$$ $$\frac{dy}{dx}$$ = y





2. The attempt at a solution
so i solve it by separation of variable and arrived at the answer of

y=$$e^{-.5x^{2}+c}$$

i am afride it is wrong, or am i just confused.

 

[lanedance]

try and show your working, and note you can put a whole equation in tex tags
$$x^3 \frac{dy}{dx} = y$$

did you separate like below?
$$\frac{dy}{y} = \frac{dx}{x^3}$$

 

[seto6]

try and show your working, and note you can put a whole equation in tex tags
$$x^3 \frac{dy}{dx} = y$$

did you separate like below?
$$\frac{dy}{y} = \frac{dx}{x^3}$$

yes.

 

[HallsofIvy]

Then you've lost a sign.

If $dy/y= dx/x^3= x^{-3}dx$ then

$$ln(y)= -(1/2)x^{-2}+ C$$
and so

$$y= e^{-.5x^{-2}+ C$$

It should be $x^{-2}$ in the exponent, not $x^2$.