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Agent_A
 one year ago
Differential Equations problem.
Solve the initial Value Problem: (see the given, below)
I have the solution, and I know that we have to use integration by parts, but I'd like a better (clearer) solution, please. Just send me the whole thing. I want to see the way you solve it, in one run. Thanks!
Agent_A
 one year ago
Differential Equations problem. Solve the initial Value Problem: (see the given, below) I have the solution, and I know that we have to use integration by parts, but I'd like a better (clearer) solution, please. Just send me the whole thing. I want to see the way you solve it, in one run. Thanks!

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Agent_A
 one year ago
Best ResponseYou've already chosen the best response.0\[\frac{ dy }{ dt } = y + 2t\] \[y(0) = 2\]

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.3As a start, multiply \(e^{t}\) through out

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.3\(\dfrac{ dy }{ dt } = y + 2t\) \(\dfrac{ dy }{ dt } y = 2t\) \(\color{red}{e^{t}}\dfrac{ dy }{ dt }  \color{red}{e^{t}}y = \color{red}{e^{t}}2t\) Now, do you notice anythign special about the left hand side ?

Jhannybean
 one year ago
Best ResponseYou've already chosen the best response.1Can this form be defined as \(\dfrac{dy}{dt}  P\cdot y = Q\) ?

Jhannybean
 one year ago
Best ResponseYou've already chosen the best response.1Oh I kind of see it now.

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.3Yes, it's indeed a linear equation..

Astrophysics
 one year ago
Best ResponseYou've already chosen the best response.2Note the integrating factor is \[e^{t}\] now what happens when you take the derivative of this \[(e^{t}y)'\]
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