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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
Take the carburizing of a steel bar to make a hard surface. To obtain the desired hardness, we require to control the diffusion of carbon into the surface and the phases obtained d
Using the example provided, Evaluate the area of the shaded region in terms of π. a. 264 - 18π b. 264 - 36π c. 264 - 12π d. 18π- 264 b. The area of the shaded r
Give an Equations with the variable on both sides ? Many equations that you encounter will have variables on both sides. Some of these equations will even contain grouping sy
Tom has five times as many marbles as Jim. together they have 42 marbles. how many marbles does each has?
i want to find the solution for exercises
a cheeseburger cost $6.39 more than a burger of $2.29, what is the difference?
Problem 1 Work through TALPAC 10 Basics (refer to attached handout). Answer the set of questions at the end of tutorial module. Problem 2 Referring to both the haul cyc
The temperature at 6 P.M. was 31°F. Through midnight, it had dropped 40°F. What was the temperature at midnight? Visualize a number line. The drop from 31° to 0° is 31°. There
If the roots of the equation (b-c)x 2 +(c-a)x +(a-b) = 0 are equal show that a, b, c are in AP. Ans: Refer sum No.12 of Q.E. If (b-c)x 2 + (c-a) x + (a-b) x have equ
A set consists of (2n+1) elements. If the number of subsets of this set which consist of at most n elements is 8192. Find out the value of n. Ans: The following set has (2n + 1
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