Ordinary differential equations UE Past Papers Questions.


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(1980) Question Category: Mathematical Calculation

Solve the IVP

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

and find the interval of validity of the solution.

Answer / Solution

UNSOLVED

(1981) Question Category: Mathematical Calculation

Show that by using polar transformation the differential equation

(x+y)dx-(x-y)dy=0

can be reduced to a variable separable differential equation

frac{dr}{d heta}=r

Answer / Solution

UNSOLVED

(1982) Question Category: Mathematical Calculation

Solve the differential equation xy`-2y=4x^{3}y^{frac{1}{2}}

Answer / Solution

UNSOLVED

(1983) Question Category: Mathematical Calculation

If f, g and h are differentiable functions, show that

W(fg,fh)=f^{2}W(g,h)

Answer / Solution

UNSOLVED

(1984) Question Category: Mathematical Calculation

Show that if p is differentiable and p(t)>0 the Wronskian W(t) of two solutions of [p(t)y`]`+q(t)y=0 is

W(t)=frac{c}{p(t)}  where c is constant.

Answer / Solution

UNSOLVED

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