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# Differential equation : is this correct? watch

1. Hi,

the problem states dy/dx = cos (x+y).

Is what I have done correct?

dy/dx = cos(x+y)

u = x + y
du/dx = 1 + dy/dx

du/dx = cos(u) + 1

du/dx = 2cos²(0.5u) following double angle formula

dx/du = 1/2cos²(0.5u)

integral(dx/du)du = integral(1/2cos²(0.5u))du

x = tan(0,5u) + C

tan⁻¹ x + C = 1/2 (x + y)

y = 2tan⁻¹ x + x + C

Is this correct?

Thanks
2. x = tan(0.5u) + C

This is correct but the answer is wrong. Can you correct it?
3. (Original post by 0-))
x = tan(0.5u) + C

This is correct but the answer is wrong. Can you correct it?
yep

y = 2tan⁻¹ x - x + C

k, thanks for the help Just thought was easier than what the question suggested, so tha tI'd probably done something wrong
4. (Original post by thegluups)
yep

y = 2tan⁻¹ x - x + C

k, thanks for the help Just thought was easier than what the question suggested, so tha tI'd probably done something wrong
Almost but you need to keep the constant included in the arctan.

x = tan(0.5u) + C --> arctan(x-C)=0.5u

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