Question

a) Let y be the solution of the equation y ′ − [(3x^2*y)/(1+x^3)]=1+x^3 satisfying the condition  y...

a)

Let y be the solution of the equation

y ′ − [(3x^2*y)/(1+x^3)]=1+x^3 satisfying the condition  y ( 0 ) = 1.

Find y ( 1 ).

b)

Let y be the solution of the equation y ′ = 4 − 2 x y

satisfying the condition y ( 0 ) = 0.

Use Euler's method with the horizontal step size  h = 1/2

to find an approximation to the value of the function

y at x = 1.

c)

Let y be the solution of the equation y ′ = 4 x + y^2

satisfying the condition y ( 0 ) = 0.

Use Euler's method with the horizontal step size  h = 1/2

to find an approximation to the value of the function

y at x = 1.

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