- #1
squareroot
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Homework Statement
okey, so i got stuck at another step in the way of solving de's.I've been studying DE of this form:
y' + P(x)y = Q(x)
Homework Equations
The Attempt at a Solution
So, first we solve y' + P(x)y=0 for y. [tex] \frac{dy}{y} = -P(x)dx [/tex] , we integrate this and get that [tex] \int \frac{1}{y}\,dy = -\int P(x)\,dx [/tex] [tex] ln(y) + C= -\int P(x)\,dx [/tex] [tex] y= e^{-C-\int P(x)\,dx} [/tex] this is my attempt to solve but the textbook says that the answer is [tex]C(x)e^{-\int P(x)\,dx } [/tex] . I don't understand that C(x)...Isn't C just a constant?Why does it depend on x?
Thank you