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There actually isn't a whole lot to do throughout this case. We'll find two solutions which will form a basic set of solutions and therefore our general solution will be as,
Example: Solve the following initial value problem
2 x2 y′′ + 3xy′ -15 y = 0,
y (1) = 0
y′ (1) = 1
Solution
We first require finding the roots to (3).
2r ( r -1) + 3r -15 = 0
2r2 + r -15 = (2r - 5)(r + 3) = 0
⇒ r1 = 5/2 and r2 = -3
Then the general solution is,
y(x) = c1x5/2 + c2 x-3
To get the constants we differentiate and plug into the initial conditions where we did back into the second order differential equations section.
y'(x) = (5/2) c1x3/2 - 3c2 x-4
0 = y(1) = c1 + c2
1 = y'(1) = (5/2)c1 + (-3) c2
By solving these equations we get:
c1 = 2/11,
c2 = -(2/11)
the actual solution is,
y(x) = (2/11) x5/2 -(2/11) c2 x-3
What is Angles? An angle is made up of two rays with a common endpoint, which is called the vertex. The sides of the angle are rays. An angle is denoted by "θ". When two li
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The form x2 - bx + c ? This tutorial will help you factor quadratics that look something like this: x 2 -7x + 12 (No leading coefficient; negative middle coefficient; p
Classify the following discrete-time signals as energy or power signals. If the signal is of energy type, find its energy. Otherwise, find the average power of the signal. X 1
Explain how we Converting Fractions to Percents ? To convert a fraction to a percent: 1. Convert the fraction to a decimal using long division. 2. Move the decimal point two p
The volume of grains in a silo at a particular time (measured in hours) is given by V (t) = 4t(3-t) m 3 . Find the rate of change of the volume of grains in the silo from first pri
Why is it important the the Enlightenment grew out of the salons and other meeting places of Europe? Who was leading the charge? Why was this significant? Where there any names or
At an office, the manager earns 40% more than a first year employees. The employee earns what fraction of the manager earnings?
multiply (1/2+1/2i) ten times
56+3
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