   Chapter 12.5, Problem 4E ### Mathematical Applications for the ...

11th Edition
Ronald J. Harshbarger + 1 other
ISBN: 9781305108042

#### Solutions

Chapter
Section ### Mathematical Applications for the ...

11th Edition
Ronald J. Harshbarger + 1 other
ISBN: 9781305108042
Textbook Problem

# In Problems 1-4, show that the given function is a solution to the differential equation. 4.   y = 4 x 3 + 2 ;        3 y   d x − x   d y = 6   d x

To determine

To prove: The function y=4x3+2 is a solution to the differential equation 3ydxxdy=6dx.

Explanation

Given Information:

The provided function is y=4x3+2 and the differential equation is 3ydxxdy=6dx.

Formula used:

Power rule of derivative is ddx(xn)=nxn1, where n is a real number.

Proof:

Consider the function, y=4x3+2

Differentiate both sides with respect to x,

dydx=ddx(4x3+2)dydx=43x31+0dydx=12x2dy=12x2dx

Consider the differential equation, 3ydxxd<

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