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Consider the following initial-value problem. (y² cos(x) - 3x²y - 6x) dx + (2y sin(x) − x³ + In(y)) dy = 0, af Let = ?х y² cos(x) - 3x²y - 6x. Integrate this partial derivative with respect to x, letting h(y) be an unknown function in y. f(x, y) = Find the derivative of h(y). h'(y) = ln (y) + h(y) Solve the given initial-value problem. X y(0) = e

Consider the following initial-value problem. (y² cos(x) - 3x²y - 6x) dx + (2y sin(x) − x³ + In(y)) dy = 0, af Let = ?х y² cos(x) - 3x²y - 6x. Integrate this partial derivative with respect to x, letting h(y) be an unknown function in y. f(x, y) = Find the derivative of h(y). h'(y) = ln (y) + h(y) Solve the given initial-value problem. X y(0) = e

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Consider the following initial-value problem. (y² cos(x) - 3x²y - 6x) dx + (2y sin(x) − x³ + In(y)) dy = 0, af Let = ?х y² cos(x) - 3x²y - 6x. Integrate this partial derivative with respect to x, letting h(y) be an unknown function in y. f(x, y) = Find the derivative of h(y). h'(y) = ln (y) + h(y) Solve the given initial-value problem. X y(0) = e
Transcribed Image Text:Consider the following initial-value problem. (y² cos(x) - 3x²y - 6x) dx + (2y sin(x) − x³ + In(y)) dy = 0, af Let = ?х y² cos(x) - 3x²y - 6x. Integrate this partial derivative with respect to x, letting h(y) be an unknown function in y. f(x, y) = Find the derivative of h(y). h'(y) = ln (y) + h(y) Solve the given initial-value problem. X y(0) = e
Use Euler's method to obtain a four-decimal approximation of the indicated value. First use h = 0.1 and then use h = 0.05. Find an explicit solution for the initial-value problem and then fill in the following tables. (Round your answers to four decimal places. Percentages may be rounded to two decimal places.) y' = 2xy, y(1) = 1; y(1.5) (explicit solution) y(x) =
Transcribed Image Text:Use Euler's method to obtain a four-decimal approximation of the indicated value. First use h = 0.1 and then use h = 0.05. Find an explicit solution for the initial-value problem and then fill in the following tables. (Round your answers to four decimal places. Percentages may be rounded to two decimal places.) y' = 2xy, y(1) = 1; y(1.5) (explicit solution) y(x) =
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