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Consider the differential equation dy/dx = 4(x + 2) - y
For the initial condition y = 3 at x = 1, the value of y at x = 1.4 obtained using Euler’s method with a step-size of 0.2 is ________ . (round off to one decimal place)
For the initial condition y = 3 at x = 1, the value of y at x = 1.4 obtained using Euler’s method with a step-size of 0.2 is ________ . (round off to one decimal place)
Correct answer is between '6.3,6.5'. Can you explain this answer?
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Consider the differential equation dy/dx = 4(x + 2) - yFor the initial...
The Euler method is given by the formula:
y_(n+1) = y_n + h*f(x_n, y_n)
where y_n is the value of y at the nth step, x_n is the value of x at the nth step, h is the step size, and f(x_n, y_n) is the value of the derivative dy/dx at the nth step.
In this case, the step size h = 0.4 since we are going from x = 1 to x = 1.4 in steps of 0.4.
Using the given initial condition y = 3 at x = 1, we can start the iteration:
x_0 = 1
y_0 = 3
At each step, we need to compute the value of the derivative dy/dx at the current step (x_n, y_n). In this case, dy/dx = 4(x - 2) - y.
Step 1: (x_1, y_1)
x_1 = x_0 + h = 1 + 0.4 = 1.4
y_1 = y_0 + h*dy/dx = 3 + 0.4*(4(1) - 2) - 3 = 3 + 0.4*(4 - 2) - 3 = 3 + 0.4*2 - 3 = 3 + 0.8 - 3 = 0.8
Therefore, at x = 1.4, y = 0.8.
y_(n+1) = y_n + h*f(x_n, y_n)
where y_n is the value of y at the nth step, x_n is the value of x at the nth step, h is the step size, and f(x_n, y_n) is the value of the derivative dy/dx at the nth step.
In this case, the step size h = 0.4 since we are going from x = 1 to x = 1.4 in steps of 0.4.
Using the given initial condition y = 3 at x = 1, we can start the iteration:
x_0 = 1
y_0 = 3
At each step, we need to compute the value of the derivative dy/dx at the current step (x_n, y_n). In this case, dy/dx = 4(x - 2) - y.
Step 1: (x_1, y_1)
x_1 = x_0 + h = 1 + 0.4 = 1.4
y_1 = y_0 + h*dy/dx = 3 + 0.4*(4(1) - 2) - 3 = 3 + 0.4*(4 - 2) - 3 = 3 + 0.4*2 - 3 = 3 + 0.8 - 3 = 0.8
Therefore, at x = 1.4, y = 0.8.
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Consider the differential equation dy/dx = 4(x + 2) - yFor the initial...
For finding y2, two iteration has to be followed.
dy/dx = 4(x + 2) - y (given differential equation)
y1 = y0 + hf(x0, y0)
= 3 + 0.2 f(1, 3)
= 3 + 0.2 [4(1 + 2) - 3]
= 3 + 0.2 (12 - 3)
= 4.8
y2 = y1 + hf{x1, y1)
= 4.8 + 0.2 f( 12, 4.8)
= 4.8 + 0.2 [4(1.2 + 2) - 4.8]
= 4.8 + 0.2 (12.8 - 4.8)
= 4.8 + 1.6 = 6.4
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Consider the differential equation dy/dx = 4(x + 2) - yFor the initial condition y = 3 at x = 1, the value of y at x = 1.4 obtained using Euler’s method with a step-size of 0.2 is ________ . (round off to one decimal place)Correct answer is between '6.3,6.5'. Can you explain this answer?
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Consider the differential equation dy/dx = 4(x + 2) - yFor the initial condition y = 3 at x = 1, the value of y at x = 1.4 obtained using Euler’s method with a step-size of 0.2 is ________ . (round off to one decimal place)Correct answer is between '6.3,6.5'. Can you explain this answer? for Civil Engineering (CE) 2024 is part of Civil Engineering (CE) preparation. The Question and answers have been prepared according to the Civil Engineering (CE) exam syllabus. Information about Consider the differential equation dy/dx = 4(x + 2) - yFor the initial condition y = 3 at x = 1, the value of y at x = 1.4 obtained using Euler’s method with a step-size of 0.2 is ________ . (round off to one decimal place)Correct answer is between '6.3,6.5'. Can you explain this answer? covers all topics & solutions for Civil Engineering (CE) 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Consider the differential equation dy/dx = 4(x + 2) - yFor the initial condition y = 3 at x = 1, the value of y at x = 1.4 obtained using Euler’s method with a step-size of 0.2 is ________ . (round off to one decimal place)Correct answer is between '6.3,6.5'. Can you explain this answer?.
Consider the differential equation dy/dx = 4(x + 2) - yFor the initial condition y = 3 at x = 1, the value of y at x = 1.4 obtained using Euler’s method with a step-size of 0.2 is ________ . (round off to one decimal place)Correct answer is between '6.3,6.5'. Can you explain this answer? for Civil Engineering (CE) 2024 is part of Civil Engineering (CE) preparation. The Question and answers have been prepared according to the Civil Engineering (CE) exam syllabus. Information about Consider the differential equation dy/dx = 4(x + 2) - yFor the initial condition y = 3 at x = 1, the value of y at x = 1.4 obtained using Euler’s method with a step-size of 0.2 is ________ . (round off to one decimal place)Correct answer is between '6.3,6.5'. Can you explain this answer? covers all topics & solutions for Civil Engineering (CE) 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Consider the differential equation dy/dx = 4(x + 2) - yFor the initial condition y = 3 at x = 1, the value of y at x = 1.4 obtained using Euler’s method with a step-size of 0.2 is ________ . (round off to one decimal place)Correct answer is between '6.3,6.5'. Can you explain this answer?.
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