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  3. a) let y be the solution of the equation y ? = sqr

a) Let y be the solution of the equation y ? = sqrt(1 ? y^2) satisfying the...

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Question

Basic Math

a)

Let y be the solution of the equation

y ? = sqrt(1 ? y^2) satisfying the condition  y ( 0 )= 0.

Find the value of the function  f ( x ) = sqrt(2)*y (x ) at x = ?/4.

(The square root in the right hand side

of the equation takes positive values and ? 1 ? y ? 1)

b)

Let y be the solution of the equation

y ? = 5 x^4 sin ?(x^5) satisfying the condition y ( 0 ) = ?1.

Find y ( (?)^1/5 ).

c)

Find the largest value of the parameter r

for which the function y = e^(rx) is a solution of the

equation y ? ? 12 y ? + 27 y = 0.

d)

Let y ? = ? 3x^2*e^(-x^3) and let y ( 0 ) = 1.

Find  ln ? ( y ( 2 ) ).

e)

Find the smallest value of the parameter r

for which the function y = e^(rx) is a solution of the

equation y ? ? 12 y ? + 27 y = 0.

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