💬 👋 We’re always here. Join our Discord to connect with other students 24/7, any time, night or day.Join Here!



Numerade Educator



Problem 3 Medium Difficulty

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


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


You must be signed in to discuss.

Nomonde N.

January 27, 2021

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

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.