Here are the questions:
http://s4.postimage.org/40e5r2xxk/n2more…
I know those 2 problems are a lot of work but i really need to understand them. Do not worry about the direction field. Just provide me with the solutions with all the steps so i can prepare for my final.
Thank you so muchhhh
http://s4.postimage.org/40e5r2xxk/n2more…
I know those 2 problems are a lot of work but i really need to understand them. Do not worry about the direction field. Just provide me with the solutions with all the steps so i can prepare for my final.
Thank you so muchhhh
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1.) y' = 3*sin(t) + 1 + y
dy/dt - y = 3*sin(t) + 1
Integrating factor = e^(∫- dt) = e^(-t)
e^(-t)*(dy/dt) - y*e^(-t) = 3*e^(-t)*sin(t) + e^(-t)
d/dt[y*e^(-t)] = e^(-t)*(3*sin(t) + 1)
y*e^(-t) = ∫e^(-t)*(3*sin(t) + 1) dt
y*e^(-t) = -1/2*e^(-t)*[3*sin(t) + 3*cos(t) + 2] + C
y = -3/2*(sin(t) + cos(t)) - 1 + C*e^(t)
dy/dt - y = 3*sin(t) + 1
Integrating factor = e^(∫- dt) = e^(-t)
e^(-t)*(dy/dt) - y*e^(-t) = 3*e^(-t)*sin(t) + e^(-t)
d/dt[y*e^(-t)] = e^(-t)*(3*sin(t) + 1)
y*e^(-t) = ∫e^(-t)*(3*sin(t) + 1) dt
y*e^(-t) = -1/2*e^(-t)*[3*sin(t) + 3*cos(t) + 2] + C
y = -3/2*(sin(t) + cos(t)) - 1 + C*e^(t)
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