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2nd order differential equations

  • Thread starter trew
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  • #1
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Homework Statement


xn4AxR5.png


Homework Equations




The Attempt at a Solution


I managed to find dy/dx as follows:
dXyGySZ.png


But I'm having difficulty finding the second derivative. I've looked at examples using the chain rule but I'm still confused.

Would someone mind shedding some light on this for me?
 

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  • #2
Orodruin
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I managed to find dy/dx as follows:
This is not particular for dy/dx. It holds if you replace y by any function. In particular, what do you get if you replace y by dy/dx?
 
  • #3
Stephen Tashi
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Homework Equations

The product rule and the chain rule are relevant equations.

But I'm having difficulty finding the second derivative.
Part of applying the product rule to find ##\frac{d^2 y}{dx^2} = \frac{d}{dx} ( \frac{dy}{dz} cos(x))## requires evaluating the factor ##\frac{d}{dx} \frac{dy}{dz}##. The chain rule, in words, says "the derivative with respect to x of a function of z is equal to the derivative of the function with respect to z times the derivative of z with respect to x". As @Orodruin pointed out, you can apply this rule when "a function of z" is ##\frac{dy}{dz}##. What do you get when you differentiate ##\frac{dy}{dz}## with respect to ##z## ?
 

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