Question

If f is the solution of x*f'(x)-f(x)=x such that f(-1)=1, find f(e^-1). Answer: -2e^-1.

Answer 1

damn lost all my typing :((

Answer 2

Yes

Answer 3

i got y = x ln(x) - x
f(e^-1) = (e^-1) ln(e^-1) - e^-1
= -e^-1 - e^-1
= -2e^-1

Answer 4

first order linear differential equation.

Answer 5

yes

Answer 6

no, you can't just solve for y'

Answer 7

that's not how you solve first order linear differential equation

Answer 8

well your answer didn't match with the given answer

Answer 9

ok, y' - (1/x) y = 1

Answer 10

multiply both sides by 1/x to reverse product rule
(1/x)y' - (1/x^2)y = 1/x

d/dx (1/x)y = 1/x
(1/x)y = ln|x| + C
y = x ln|x| + Cx

given f(-1) = 1
1 = (-1) ln|-1| + C(-1)
1 = -C
C = -1

y = x ln|x| - x
plug in e^-1 for x gives -2e^-1

Answer 11

have you taken differential equation before?

Answer 12

Yes. But this problem isn't Differential Equations.