Question

a. Solve the differential equation y prime equals the product of 4 times x and the square root of the quantity 1 minus y squared. b. Explain why the initial value problem y prime equals the product of 4 times x and the square root of the quantity 1 minus y squared with y(0) = 4 does not have a solution.

Answer 1

1/√1-y2 (use of inverse SINE)

sin−1(y)=2x2+C

4= sin (c)

Answer 2

Explanation:

Given is a differential equation as:

`y'=4x√(1-y^2)`

We can solve this by separation of variables method

`(dy)/(√(1-y^2) ) =4xdx\\sin^(-1) y = 2x^2+C`

To find C:

Given y(0) =4

Substitute x=0 and y =4

sin inverse of 4 = C

But sin inverse is valid only for values between -1 and 1

Hence C is not a real value

No solution for this.