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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

Calculus For The Life Sciences
Calculus For The Life Sciences
2nd Edition
ISBN:9780321964038
Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Chapter9: Multivariable Calculus
Section9.2: Partial Derivatives
Problem 31E
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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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ISBN:
9780321964038
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GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
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