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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
STATISTICS AND PROBABILITY : Statistics are the only tools by which an opening can be cut through the formidable thicket of difficulties that bars the path of
all formulas of plane figures
l+bx2= 5000+100x2
1. In 1900, a certain country's population was 77,977,459 and it's area was 2,821,924 square miles, In 2000, the country's population was 283,575,229 and its area was 3,551,003 sq
assignment of mathematics in b.sc. 1sem
Deflation Indexes may be utilized to deflate time series so that comparisons among periods may be made in real terms. This is a process of decreases a value measured in cur
In the prior section we looked at Bernoulli Equations and noticed that in order to solve them we required to use the substitution v = y 1-n . By using this substitution we were cap
give me the derivation of external division of sectional formula using vectors
Higher-Order Derivatives It can be seen that the derivative of a function is also a function. Considering f'x as a function of x, we can take the derivative
COMMUNICATING THE MEANING OF ADDITION : One of the characters in a novel written by the Malayalam writer Vaikom Muhammed Basheer was asked by his teacher, "How much is one and on
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