Question

Помогите решить плиз y''+8y'-9y=0

Answer 1

9y-9y=0 
0=0,я думаю так

Answer 2

Solving the Differential Equation y'' + 8y' - 9y = 0

To solve the given differential equation y'' + 8y' - 9y = 0, we can use the method of characteristic roots. This method involves assuming a solution of the form y = e^(rx), where r is a constant to be determined. Let's go through the steps to find the general solution.

Step 1: Find the characteristic equation The characteristic equation is obtained by substituting y = e^(rx) into the given differential equation. We get: r^2 e^(rx) + 8r e^(rx) - 9 e^(rx) = 0

Step 2: Simplify the equation Divide through by e^(rx) to simplify the equation: r^2 + 8r - 9 = 0

Step 3: Solve the quadratic equation Solve the quadratic equation r^2 + 8r - 9 = 0. This can be factored as (r + 9)(r - 1) = 0, giving us two possible values for r: r = -9 and r = 1.

Step 4: Find the general solution The general solution is given by a linear combination of the two solutions: y(x) = C1 e^(-9x) + C2 e^x

Where C1 and C2 are arbitrary constants that can be determined by applying initial conditions, if provided.

That's it! We have found the general solution to the given differential equation y'' + 8y' - 9y = 0.