Ordinary differential equations UE Past Papers Questions.


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(2050) Question Category: Mathematical Calculation

Determine whether the given pair of functions is linearly independent or linearly dependent.

  1. f(t)=t^{2}+5t,,g(t)=t^{2}-5t
  2. f( heta)=cos,3 heta,,g( heta)=4,cos^{3}, heta-3,cos, heta
  3. f(t)=e^{{lambda} t}cos,mu t,,g(t)=e^{{lambda} t}sin,mu t,,mu eq 0

Answer / Solution

UNSOLVED

(2942) Question Category: Mathematical Calculation

Solve x"+3x`+2x=30e^{2t}

  1. Use undetermined coefficients method
  2. Use variation of parameters method

Answer / Solution

UNSOLVED

(2943) Question Category: Mathematical Calculation

Reduce the Cauchy-Euler differential equation 2x^{2}y"+3xy`-y=0 to constant coefficients second order homogenous differential equation.

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(3568) Question Category: Mathematical Calculation

Check the exactness and solve the given differential equation

(3x^{2}-y^{2})dy-2xydx=0

Answer / Solution

UNSOLVED

(3569) Question Category: Mathematical Calculation

Use the Laplace transform to find the solution of the following system

left{egin{matrix} y`+x=1\ x`-y=-4e^t & x(0)=0,&y(0) =0 end{matrix} ight.

Answer / Solution

UNSOLVED

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