Determine if the differential equation (3x^2e^y - 2x)dx - (2y - x^3e^y)dy = 0 is exact. If exact, find the particular solution when y(2) = 0? In writing your final answer, follow the format 2x^3e^x-3y^2+x^3y-2xy^2=c. If it involved product of a variable and exponential e, write first the variable followed by the exponential e. The constant of integration c is written on the right side of the equation. Strictly no spaces between symbols. If in a term it involved x and y, write x first followed by y whatever the exponent be. Do not use grouping symbols for the product or multiplication symbol. All letters should be in small letter and the order of the addends is not necessary. Use the symbol (^) caret to denote the exponent of the variable.

Determine if the differential equation (3x^2e^y - 2x)dx - (2y - x^3e^y)dy = 0 is exact. If exact, find the particular solution when y(2) = 0? In writing your final answer, follow the format 2x^3e^x-3y^2+x^3y-2xy^2=c. If it involved product of a variable and exponential e, write first the variable followed by the exponential e. The constant of integration c is written on the right side of the equation. Strictly no spaces between symbols. If in a term it involved x and y, write x first followed by y whatever the exponent be. Do not use grouping symbols for the product or multiplication symbol. All letters should be in small letter and the order of the addends is not necessary. Use the symbol (^) caret to denote the exponent of the variable.

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.

Chapter11: Differential Equations

Section11.1: Solutions Of Elementary And Separable Differential Equations

Problem 16E: Find the general solution for each differential equation. Verify that each solution satisfies the...

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