Question

Find y as a function of x if y'''+81 y'=0
y'(0)=-6
y"(0)=-54
y"(0)=243
y(x)=?

Answer 1

To find y as a function of x, solve the differential equation y'''+81y'=0 using the given initial conditions and the general solution.

Step-by-step explanation:

To find the function y as a function of x, we need to solve the differential equation y'''+81y'=0.

First, we solve the auxiliary equation r^3+81r=0 to find the roots, which are r=0, r=9i, and r=-9i.

Since we have complex roots, the general solution is y(x) = c1 + c2*cos(9x) + c3*sin(9x), where c1, c2, and c3 are constants determined by the initial conditions.

Using the given initial conditions, we can find the values of the constants and obtain the specific solution.