Let y be the solution of the equation
a)
y ′ = 2 x y, satisfying the condition y ( 0 ) = 1.
Find the value of the function f ( x ) = ln ( y ( x ) )
at the point x = 2.
b)
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 = π/4.
(The square root in the right hand side
of the equation takes positive values and − 1 ≤ y ≤ 1)
c)
Let y be the solution of the equation
y ′ + (3x^2y)/(1+x^3)=(e^x)/(1+x^3) satisfying the condition y ( 0 ) = 1.
Find ln ( 2 y ( 1 ) ).
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