Find the specific antiderivative that satisfies the following conditions: dy = 3x dx -2 + 6x - 7; y(1) = 8.

College Algebra (MindTap Course List)
12th Edition
ISBN:9781305652231
Author:R. David Gustafson, Jeff Hughes
Publisher:R. David Gustafson, Jeff Hughes
Chapter2: Functions And Graphs
Section2.6: Proportion And Variation
Problem 18E
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Find the specific antiderivative that satisfies the following conditions:
dy
-2
3x
+ 6x¯1 – 7; y(1) = 8.
dx
y =
Transcribed Image Text:Find the specific antiderivative that satisfies the following conditions: dy -2 3x + 6x¯1 – 7; y(1) = 8. dx y =
Expert Solution
Step 1

Given Data:

Differential equation: dydx=3x-2+6x-1-7 ......(1)

Condition: y(1)=8

 

The antiderivative can be obtained by integrating the given equation.

1dy=3x-2dx+6x-1-7dx1dy=3x-2dx+6x-1dx-7dxy=3x-2+1-2+1+6lnx+7x+Cy=3x-1-1+6lnx+7x+Cy=-3x-1+6lnx+7x+C ......2

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