Find solution of y′(t) = ky(t) with y(1) = 5 y′(1) = 4. y = Ce^(kt)

postillan4 2020-12-06 Answered

Find solution of y(t)=ky(t) with y(1)=5y(1)=4. y=Cekt

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Expert Answer

Szeteib
Answered 2020-12-07 Author has 102 answers

Write as dydt=ky.
dyy=kdt+c.
ln(y)=kt+c.
Therefore k=ln(y)ct. When y=5,t=1,ln(5)=k+c.k=ln(5)c.
y=ekt+c=et(ln(5)c)+c.dydt=(ln(5)c)et(ln(5)c)+c.
When dydt=4,t=1:4=5(ln(5)c).ln(5)c=0.8, so c=ln(5)0.8.
Therefore k=0.8.
So y=e0.8t+ln(5)0.8=5e0.8t(0.4493)=2.2466e0.8t approx.

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