Solve the differential equation y' =4x sqrt(1-y^2)

The general solution to this differential equation is    for x such that ======explanation: assuming this diff. eqn. has a derivative of y with respect to x, rewrite so that we have y' = dy/dx    this is a separable differential equation as the derivative can be written as a product of two factors: a function of y and and a function x (the two variables we are differentiating). the factors are 4x and  √(1-y²).  to solve this differential equation for the general solution, we must separate the variables. separation of the variables can be done by treating dy/dx as a fraction. move the dx with the function-of-x  factor and move the function-of-y factor with the dy:     now integrate both sides    on the left-hand side, note that  so it follows that the antiderivative of  is  .on the right-hand side, we use the power rule for antiderivatives    note here that since by definition  , we must have we can solve for y by taking the sine of both sides of the equation, resulting in a cancellation  on the left-hand side    that is the general solution for