Question

Let y be the solution of the equation a) y ′ = 2 x y, satisfying...

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 ) ).

Math   Calculus   
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