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.
