# Maths Question

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The question is:

I have got an answer which I think is right. But the answer in the back is different.

Code:

Find y in terms of x given that dy/dx + 2y = sinx and that the solution curve passes through the origin.

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#3

(Original post by

The question is:

I have got an answer which I think is right. But the answer in the back is different.

**mikesgt2**)The question is:

Code:

Find y in terms of x given that dy/dx + 2y = sinx and that the solution curve passes through the origin.

I = e^2x

e^2x dy/dx + 2e^2x y = e^2x sinx

e^2x y = integral e^2x sinx dx == K

u=e^2x => du/dx = 2e^2x

dv/dx = sinx => v=-cosx

K = -e^2x cosx + 2 {integral e^2x cosx dx == L}

a = e^2x => da/dx= 2 e^2x

db/dx = cosx => b=sinx

L = e^2x sinx - 2 integral e^2x sinx == e^2x sinx - 2K

K = -e^2x cosx + 2 e^2x sinx - 4K

5K = 2 e^2x sinx - e^2x cosx = e^2x (2six - cosx)

=> e^2x y = 1/5 e^2x (2sinx - cosx)

=> y = 1/5 (2sinx - 1osx + C)

0 = 2/5 sin 0 -1/5 sin 0 + 1/5 C

=> C = 1

=> y = 1/5 (2sinx - cosx +1)

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#4

**mikesgt2**)

The question is:

Code:

Find y in terms of x given that dy/dx + 2y = sinx and that the solution curve passes through the origin.

0

Elpaw...

I got what you got... apart from I just realised I made a stupid mistake in calculating the constant of integration.

But... the answer in the back is:

y = 1/5 ( 2sinx - cosx +e^(-2x) )

I got what you got... apart from I just realised I made a stupid mistake in calculating the constant of integration.

But... the answer in the back is:

y = 1/5 ( 2sinx - cosx +e^(-2x) )

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#6

(Original post by

Elpaw...

I got what you got... apart from I just realised I made a stupid mistake in calculating the constant of integration.

But... the answer in the back is:

y = 1/5 ( 2sinx - cosx +e^(-2x) )

**mikesgt2**)Elpaw...

I got what you got... apart from I just realised I made a stupid mistake in calculating the constant of integration.

But... the answer in the back is:

y = 1/5 ( 2sinx - cosx +e^(-2x) )

=> e^2x y = 1/5 e^2x (2sinx - cosx)

__+ C__=> y = 1/5 (2sinx - cosx) + C e^-2x

dot dot dot

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