# How do you find the particular solution to #ysqrt(1-x^2)y'-x(1+y^2)=0# that satisfies y(0)=sqrt3?

##### 1 Answer

Use the separation of variables method, integrate both sides, and then use the specified point to evaluate the constant.

#### Explanation:

Given:

Use the notation

Move the second term to the right side:

Multiply both sides of the equation by

Integrate both sides:

Multiply both sides by 2:

Use the exponential function:

Adding a constant in the exponent is the same as multiplying by a constant:

Subtract 1 from both sides:

Square root both sides:

Use the point to solve for C, substitute 0 for x and

The above equation can only be true, if we can drop the

Square both sides and solve for C:

Substitute