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# Differential equations help watch

1. Hi I am stuck on two questions. I am a bit stuck on where to start.

1) Solve the differential equation
(tcos(xt)+(2xt^2)-(x^-2))dx/dt +xcos(xt) = 1-(2tx^2)
subject to initail condition x=pi when t=1

2) Solve the differential equation x.dy/dx +y +xy = e^-x
with initial consition y=0 when x = 1

For 1) I thought to find out if it is exact. By using p and q, differentiating to see if exact. Then integrating to find out h? But i think that is wrong.

For 2) I thought dividing it through by x and rearranging to get dx/dy + y(1/x + 1) = e^-x
and then using 1/x + 1 as the integrating factor?
Can someone help me
Thank you
2. 2) Your idea is correct:
dy/dx + y(1/x + 1) = (e^-x)/x you mean.

1) Is the question typed correctly?
3. (Original post by vc94)
dy/dx + y(1/x + 1) = (e^-x)/x you mean.

1) Is the question typed correctly?
Hi,
thank you.
I shall try number 2 then.
And no it wasnt typed correctly.
Thank you for spotting. I have fixed it now.
Any help is good

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