Question

Using separation of variables technique, solve the following differential equation with initial conditions dy/dx = e^{2x+3y} and y(0) = 1. (Hint: Use a property of exponentials to rewrite the differential equation so it can be separated.) The solution is: A. 1/3 e^{-3y} = 1/2 e^{2x} - 1/2 + 1/3 e^{-3} B. -1/3 e^{-3y} = 1/2 e^{2x} - 1/2 - 1/3 e^{-3} C. -1/3 e^{-3y} = 1/2 e^{2x} - 5/6 D. 1/3 e^{-3y} = 1/2 e^{2x} - 1/2 e^2 + 1/3 E. -1/3 e^{-3y} = 1/2 e^{2x} - 1/3 - 1/2 e^2

          Using separation of variables technique, solve the following differential equation with initial conditions dy/dx = e^{2x+3y} and y(0) = 1. (Hint: Use a property of exponentials to rewrite the differential equation so it can be separated.)
The solution is:
A. 1/3 e^{-3y} = 1/2 e^{2x} - 1/2 + 1/3 e^{-3}
B. -1/3 e^{-3y} = 1/2 e^{2x} - 1/2 - 1/3 e^{-3}
C. -1/3 e^{-3y} = 1/2 e^{2x} - 5/6
D. 1/3 e^{-3y} = 1/2 e^{2x} - 1/2 e^2 + 1/3
E. -1/3 e^{-3y} = 1/2 e^{2x} - 1/3 - 1/2 e^2

Using separation of variables technique, solve the following differential equation with initial conditions dy/dx = e^2x+3y and y(0) = 1. (Hint: Use a property of exponentials to rewrite the differential equation so it can be separated.)
The solution is:
A. 1/3 e^-3y = 1/2 e^2x - 1/2 + 1/3 e^-3
B. -1/3 e^-3y = 1/2 e^2x - 1/2 - 1/3 e^-3
C. -1/3 e^-3y = 1/2 e^2x - 5/6
D. 1/3 e^-3y = 1/2 e^2x - 1/2 e^2 + 1/3
E. -1/3 e^-3y = 1/2 e^2x - 1/3 - 1/2 e^2

Added by Lidia R.

Calculus: Early Transcendentals

James Stewart 8th Edition

Instant Answer

Solved by Expert William Semus

08/12/2023

Step 1

First, we use separation of variables technique to rewrite the differential equation as: dy/e^(3y) = e^(2x) dx Show more…

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Using separation of variables technique, solve the following differential equation with initial conditions dy/dx=e^(2x+3y) and y(0)=1. (Hint: Use the property of exponentials to rewrite the differential equation and separate it.) The solution is: