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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
my daughter is having trouble with math she cant understand why please help us
If the following terms form a AP. Find the common difference & write the next 3 terms3, 3+ √2, 3+2√2, 3+3√2.......... Ans: d= √2 next three terms 3 + 4 √ 2 , 3 + 5√ 2 ,
v=u+at s=ut+1/2at^2
1. Four different written driving tests are administered by a city. One of these tests is selected at random for each applicant for a drivers license. If a group of 2 women and 4 m
logical reasoning
#question.Find the slope of the line that passes through (7, 3) and (9, 6). Simplify your answer and write it as a proper fraction, improper fraction, or integer. .
Special Forms There are a number of nice special forms of some polynomials which can make factoring easier for us on occasion. Following are the special forms. a 2 + 2ab +
5/7+5/14
We know that 2 4 = 16 and also that 2 is referred to as the base, 4 as the index or power or the exponent. The same if expressed in terms of logarithms would be log 2
i need help with 3x+5y=7 2x-5y=8
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