Finding the General Solution for xX' = aX

[naspek]

Question: find the general solution of xX' = aX

i know it's kinda simple ode.. but, i just don't know y i can't get the correct answer..

solution..

xX' = aX
x dX/dx = aX
d/dx X = aX/x
X = ∫aX/x dx
X = aX ln |x| + C

the general solution is Ax^a

problem : i can't get the correct answer..

 

[lanedance]

is X a function x? if so that's prettty messy notation

how about starting with
$$xy'(x) = ay$$

then
$$x\frac{dy}{dx} = ay$$

the idea when rearranging is to "separate" the DE, so group all the y's on one side & x's on the other side - if you can do that it means its a "seperable DE"
$$\frac{dy}{x} = a\frac{dx}{x}$$

now try intergating both sides