Sketch a few members of the straight lines through the origin. By eliminating parameters, derive a differential equation which describes this family.

Attempt

(since there are infinite gradients)

but the correct answer was: . I am not sure why.

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- Oct 25th 2010, 05:27 AMSyNtHeSiSDifferential equation for straight lines through origin
Sketch a few members of the straight lines through the origin. By eliminating parameters, derive a differential equation which describes this family.

Attempt

(since there are infinite gradients)

but the correct answer was: . I am not sure why. - Oct 25th 2010, 05:36 AMHallsofIvy
Well, your answer "dy/dx= m" isn't correct because you have not eliminated the parameter m!

From the original equation, y= mx, m= y/x which gives dy/dx= y/x. - Oct 25th 2010, 08:57 AMSyNtHeSiS
Thanks. If instead the question was: find the differential equation for the straight lines through the point (2,3), what would the procedure be?

I tried using:

y = mx + c

3 = 2m + c

but differentiating it obviously wouldnt work, since there are only constants - Oct 25th 2010, 11:47 AMmr fantastic
- Sep 5th 2014, 09:46 AMHiroshiRe: Differential equation for straight lines through origin
y=mx+c

Since, c=0

m=y/x

Differentiating on both sides....

0=y dx - x dy / y²

1 dx/y - x dy/y² =0

1 dx/y = x dy/ y²

1 dx / x = 1 dy / y

y/x = dy/dx

And that's your required answer ��