Ordinary differential equations UE Past Papers Questions.


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(1911) Question Category: Mathematical Calculation

Find a series solution of the equation , y"-y=0 about x_0=0..

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(1912) Question Category: Mathematical Calculation

Use the Laplace transforms to find the solution of the differential equation y"-3y`+2y=e^{-4t}, y(0)=1, y`(0)=5.

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(1913) Question Category: Mathematical Calculation

Find a fundamental set of solutions of x`=egin{pmatrix} -5 & 1\ 4& -2 end{pmatrix}x, x(0)=inom{1}{2} and draw a phase potrait for the system.

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(1914) Question Category: Mathematical Calculation

Solve the following IVP and find the interval of validity of the solution

  1. frac{dy }{dx}=e^{-y}(2x-4), y(5)=0
  2. frac{dy }{dx}=6y^{2}x, y(1)=frac{1}{25}
  3. y`=frac{xy^{3}}{sqrt{1+x^{2}}}, y(0)=-1
  4. frac{dr}{d heta}=frac{r^{2}}{ heta}, r(1)=2

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(1915) Question Category: Mathematical Calculation

Find the solution and interval of validity to the following IVP

  1. frac{2ty}{t^{2}+1}-2t-(2-ln(t^2+1))y`=0
  2. y`+frac{4}{x}y=x^{3}y^{2}, y(2)=-1, x>0.

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