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.

Step-by-step explanation:

Given is a differential equation as:

We can solve this by separation of variables method

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.

this linear equation would have just one solution.

step-by-step explanation:

the reason why this would have one solution is that it is an expression with just one variable. since that variable is not raised to a power, it will always have just one solution.