# Thread: Forming a Differential Equation

1. ## Forming a Differential Equation

I tried to solve the following question :-

y = c1(t-c2)^2 and y = c(t-(1/c))^2

I got stuck at the substitution to write them in the form of y' and y''. Even after giving my best try I couldn't eliminate 't' from the expression.The answer is in the form of y and y'' for 1st and y' for 2nd My expression was all right except for that 't' thing. What technique and approach should I use for solving these type of questions?

2. Originally Posted by Altair
I tried to solve the following question :-

y = c1(t-c2)^2 and y = c(t-(1/c))^2

I got stuck at the substitution to write them in the form of y' and y''. Even after giving my best try I couldn't eliminate 't' from the expression.The answer is in the form of y and y'' for 1st and y' for 2nd My expression was all right except for that 't' thing. What technique and approach should I use for solving these type of questions?
Differentiating either twice will give y'' independent of t, but presumably that
is not what you want. In that case your question is incomprehensible
consider reformulating it more clearly.

RonL

3. My problem is that....

On differentiating once the answer comes in the form of 't'. I have to form a differential equation in terms of y' and y''. This, when done by simple substitution gives answer in terms of y',y'' and t.

Or please solve these two questions for me. Please form the differential equations.

4. Originally Posted by Altair
My problem is that....

On differentiating once the answer comes in the form of 't'. I have to form a differential equation in terms of y' and y''. This, when done by simple substitution gives answer in terms of y',y'' and t.

Or please solve these two questions for me. Please form the differential equations.
So there are two questions?

$\displaystyle y = c_1(t-c_2)^2$

$\displaystyle y'=2 c_1 (t-c_2)$

$\displaystyle y'' = 2 c_1$

The other is similar

RonL

5. Thanks a lot.