- #1

karush

Gold Member

MHB

- 3,269

- 5

$\tiny{2.1.{13}}$

$\textsf{Find the solution of the given initial value problem}$

$$y'-y=2te^{2t}, \quad y(0)=1$$

$\textit{Find u(x)}$

$$\displaystyle\exp\int -1 dt =e^{ t^{-1}}$$

$\textit{multiply thru with $e^{ t^{-1}}$} $

$$ e^{ t^{-1}}y'- e^{ t^{-1}}y=2te^{t}$$

ok this isn't uv'+u'v

$\textit{W|A}$

$$\color{red}{c_1e^t+2e^{2t}t-2e^{2t}}$$

$\textsf{Find the solution of the given initial value problem}$

$$y'-y=2te^{2t}, \quad y(0)=1$$

$\textit{Find u(x)}$

$$\displaystyle\exp\int -1 dt =e^{ t^{-1}}$$

$\textit{multiply thru with $e^{ t^{-1}}$} $

$$ e^{ t^{-1}}y'- e^{ t^{-1}}y=2te^{t}$$

ok this isn't uv'+u'v

$\textit{W|A}$

$$\color{red}{c_1e^t+2e^{2t}t-2e^{2t}}$$

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