   Chapter 12.5, Problem 2E ### 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. 2.   y = x 3 ;        3 y − x y ' = 0

To determine

To prove: The function y=x3 is a solution to the differential equation 3yxy=0.

Explanation

Given Information:

The provided function is y=x3 and the differential equation is 3yxy=0.

Formula used:

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

Proof:

Consider the function, y=x3

Differentiate both sides with respect to x,

dydx=ddx(x3)y=3x31=3x2

Consider the differential equation, 3yxy

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