Question

Find y as a function of x if y′′′−11y′′+30y′=60ex if

y(0) = 28, y'(0) = 25, and y''(0) = 21.
y(x) = ??

Answer 1

To find y as a function of x, solve the given differential equation using the method of undetermined coefficients and apply initial conditions.

Step-by-step explanation:

To find y as a function of x, we need to solve the given differential equation. The equation is y′′′ − 11y′′ + 30y′ = 60ex. We can solve this equation using the method of undetermined coefficients. Let's follow the steps:

1. First, find the homogeneous solution of the equation by solving the characteristic equation r³ - 11r² + 30r = 0.
2. Next, find the particular solution by assuming a general form for yp(x) based on the form of the non-homogeneous term 60ex.
3. Combine the homogeneous solution and particular solution to get the general solution of the equation.
4. Apply the initial conditions y(0) = 28, y'(0) = 25, and y''(0) = 21 to find the specific solution of the equation.

The result will be the equation y(x) = ... (specific solution).