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# Determine whether the differential equation is linear.$ue^t = t + \sqrt t \frac {du}{dt}$

## $$u^{\prime}+P(t) u=Q(t)$$

#### Topics

Differential Equations

### Discussion

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NN

Nomonde N.

January 27, 2021

(x^2+1)dy/dx+3xy-3x=0 integration factor

##### Catherine R.

Missouri State University

##### Heather Z.

Oregon State University

##### Kristen K.

University of Michigan - Ann Arbor

Lectures

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### Video Transcript

We know that first order Lanier differential equations could be put in the form. Do you? Why, over DX, the derivative plus pee vacs times. Why is Q backs? This is the formula that was listed in the textbook chapter. Now what we know is that it's imperative that we rewrite what has been given in the original prop. So in other words, let's take the squirt of tea. Do you do t bring the You eat the power of tea over to the other sides and this case has been subtracted, and now we're sitting this equal to negative t. Now we can divide by square root of tea in order to end up with D'You over d t minus you times each. The tea over sward of G is negative square root of teeth. Therefore, we know that, yes, this is a linear differential equation.

#### Topics

Differential Equations

##### Catherine R.

Missouri State University

##### Heather Z.

Oregon State University

##### Kristen K.

University of Michigan - Ann Arbor

Lectures

Join Bootcamp