Find the general solution to the homogeneous differential equation. d2ydx2−1dydx−30y=0 d2ydx2−1dydx−30y=0 use c1c1 and c2c2 in your answer to denote arbitrary constants, and enter them as c1 and c2.

The general solution of second order homogeneous differential equation is

Step-by-step explanation:

To find the general solution of this second order homogeneous differential equation we are going to use this Theorem:

Given the differential equation , consider the quadratic polynomial , called the characteristic polynomial. Using the quadratic formula, this polynomial always has one or two roots, call them and . The general solution of the differential equation is:

(a) if the roots and are real numbers and .

(b) , if is real.

(c) , if the roots and are complex numbers and

Applying the above Theorem we have:

The characteristic polynomial is and we find the roots as follows:

The roots of characteristic polynomial are and

Therefore the general solution of second order homogeneous differential equation is

-7

step-by-step explanation:

x^2 + 18x + 74 = (x + 9)^2 - 81 + 74

= (x + 9)^2 - 7.

so q = -7.

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step-by-step explanation: