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# second order differential equations watch

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1. Can someone show me how to do the following please.

1.) dy/dx = y(x+2y) / x(y+2x), y=vx

2.) (x+y)dy/dx = x^2 + xy + x + 1, y=v-x

3.) x^2(d^2y/dx^2) + x(dy/dx) + y = 0, x=e^v
2. 1) dy/dx = y(x+2y) / x(y+2x), y=vx

y = vx
dy/dx = x(dv/dx) + v

y(x+2y) / x(y+2x)
= vx(x+2vx)/ x(vx+2x)
= v(1+2v)/(v+2)

-> x(dv/dx) + v = v(1+2v)/(v+2)
-> x(dv/dx) = (v^2 - v)/(v+2)
-> (v+2)/(v^2 - v) dv = dx/x

I guess you can do it from now.
3. The others just do it simliarly, I think you'll get the answer.

After you get v = f(x), then subsitute into y = vx to get y = g(x)
4. K thanks BCHL85, i'll give them a go.

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Updated: February 20, 2006
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