Ordinary differential equations UE Past Papers Questions.


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(3570) Question Category: Mathematical Calculation

Solve the initial value problem and sketch the plane for the system.

left{egin{matrix} x_{1}^{`}=x_{1}+2x_{2}\ x_{2}^{`}=3x_{1}+2x_{2} end{matrix} ight.

Given that x1(0)=0  and x2(0)=-4.

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(3571) Question Category: Mathematical Calculation

Briefly explain the meaning of implicit and explicit solutions of a differential equation . Use the given differential equation to show the difference between implicit and explicit solution.

y`=frac{x}{y^{`}} ,, y(1)=2)

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(3572) Question Category: Mathematical Calculation

Solve the following Bernoulli differential equation

2y`+(tan,x)y=frac{(4x+4)^{2}y^{3}}{cos,x}

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(3573) Question Category: Mathematical Calculation

Use the method of variation to parameters to solve the IVP

(x^2-1)y``+4xy`+2y=frac{2}{x+1}, , y(0)=-1, , y`(0)=-5

then state the interval of the validity

y_{1}=frac{1}{x-1},,y_2=frac{1}{x+1}

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(3574) Question Category: Mathematical Calculation

  1. i. Define the terms order, degree and linearity of differential equations
  1. State the existence and uniqueness theorem for a first order initial value problem y`=f(x,y),,,y(x_0)=y_0.
  1. Suppose that n eq 0 or n eq 1. Show that the transformation v=y^{1-n}  reduces the Bernoulli equation

frac{dy}{dx}+P(x)y=Q(x)y^{n}  to a linear equation in V.

  1. Solve the following initial valua problem and find the interval of validity for the solution.

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

Answer / Solution

UNSOLVED

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