Question

Solve the differential equation Initial Value Problem:
dy/dt=-y+5 , y(0)=Yo

Answer 1

where Yo=\[y _{0}\]

Answer 2

this is a separable differential equation\[\frac{\text{d}y}{-y+5}=\text{d}t\]integrate

Answer 3

okay I did that but in the back of the textbook it says the answer is \[y=5+(y _{0}-5)e ^{-t}\]

Answer 4

and I have no idea how that happened

Answer 5

well we have\[\frac{-\text{d}y}{-y+5}=-\text{d}t\]\[\ln(5-y)=-t+c\]apply exp\[5-y=ae^{-t}\]

Answer 6

but why did you multiply both sides by -1?

Answer 7

ohhh okay nevermind

Answer 8

I'm assuming a is y0?

Answer 9

\[\ln(5-y)=-t+c\]apply exp\[5-y=e^ce^{-t}\]let \(a=e^c\) it does'nt matter because e^c is a constant

then apply the initial value\[5-y_0=ae^0=a\]\[a=5-y_0\]

Answer 10

im having same problems i guess your taking differential equation & linear algebra also.

Answer 11

oh okay thanks mukushla, you helped me out a lot

Answer 12

:)