Ordinary differential equations UE Past Papers Questions.


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(1995) Question Category: Mathematical Calculation

Solve the cauchy euler differential equation x^{2}y'-2xy`+2y=0

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(1996) Question Category: Mathematical Calculation

Solve the initial value problem frac{dy}{dx}=frac{y^{2}}{x},,,y(1)=2

And find the interval of validity of the solution.

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UNSOLVED

(1997) Question Category: Mathematical Calculation

Solve the differential equation 6y`-2y=xy^{4},,,y(0)=-2.

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UNSOLVED

(1998) Question Category: Mathematical Calculation

If y_{1} and y_{2} are linearly independent solutions of t^{2}y'- 2y`+(3+t)y=0

And if W(y_{1},y_{2})(1)=2, find the value of W(y_{1},y_{2})(4).

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(1999) Question Category: Mathematical Calculation

Consider the initial value problem

y'+2y`+6y=0,,,,, y(0)=2, y`(0)=alpha geq 0

  1. Find the solution y(t) of this problem
  2. Find alpha so that y=0 when t=1.
  3. Find as a function of alpha, the smallest positive value of  t for which y=0.
  4. Determine the limit of the expression found in part (iii) as alpha ightarrow infty

Answer / Solution

UNSOLVED

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