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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
Graphical Method While drawing the graph on a natural scale, the independent variables are marked along the horizontal line and corresponding dependen
1. A psychologist developed a test designed to help predict whether production-line workers in a large industry will perform satisfactorily. A test was administered to all new empl
Illustration : Solve the following IVP. Solution: First get the eigenvalues for the system. = l 2 - 10 l+ 25 = (l- 5) 2 l 1,2 = 5 Therefore, we got a
How will the decimal point move when 245.398 is multiplied by 100? It is moved two places to the right. While multiplying by multiples of 10, the decimal point is moved to the
HOW MANY SHARES CAN I BUY WITH 1000 DOLLARS
1) Find the maxima and minima of f(x,y,z) = 2x + y -3z subject to the constraint 2x^2+y^2+2z^2=1 2) Compute the work done by the force ?eld F(x,y,z) = x^2I + y j +y k in moving
Solve 3 + 2 ln ( x /7+3 ) = -4 . Solution This initial step in this problem is to get the logarithm by itself on one side of the equation along with a coefficient of 1.
what is 3 divided by 4
MATHEMATICS - IN OUR LIVES : What is the most obvious example of mathematics in your life? To many of us it is the maths that we studied in school. But is that all the mathemat
Now we need to move onto something called function notation. Function notation will be utilized heavily throughout most of remaining section and so it is important to understand i
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