Solve for y. -1 = 8+3y Simplify you answer as much as possible.
2 answers:
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Answer:
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:
<em>Given the differential equation , consider the quadratic polynomial
, called the</em><em> characteristic polynomial.</em><em> Using the quadratic formula, this polynomial always has one or two roots, call them
and
. The general solution of the differential equation is:</em>
<em>(a) if the roots
and
are real numbers and
.</em>
<em>(b) , if
is real.</em>
<em>(c) , if the roots
and
are complex numbers
and
</em>
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