Find the particular solution of the differential equation that satisfies the initial condition. (Enter your solution as an equation.) Differential Equation Initial Condition YV9 - x² Y - xV144 – y² = 0 y(0) - 12

Use the problem below Discuss, and illustrate with examples, how to solve differential equations of the forms dy/dx = f(x) and d?y/dx2 = f(x). and (2) and (3) of this section. dy = f(x, y) Solve: (2) dx Subject to: y(x,) = Yo d?y Solve: fx, у, у) (3) dx2 y(x,) = Yo, y'(x,) = y, Subject to: Find a function whose second derivative is y" = 12x – 2 at each point (x, y) on its graph and y = -x + 8 is tangent to the graph at the point corresponding to x = 1. y =

solve the differential equation

Using separation of variables, solve the differential equation, Use C to represent the arbitrary constant. y2: (9+x1)- dy 3 dx Y