Chapter 2.3, Problem 128E

### Calculus of a Single Variable

11th Edition
Ron Larson + 1 other
ISBN: 9781337275361

Chapter
Section

### Calculus of a Single Variable

11th Edition
Ron Larson + 1 other
ISBN: 9781337275361
Textbook Problem

# Differential Equations In Exercises 127—-130, verify that the function satisfies the differential equation. ( A differential equation in x and y is an equation that involves x, y, and derivatives of y.)Function Differential Equation y = 2 x 3 − 6 x + 10 − y " − x y " − 2 y ' = − 24 x 2

To determine

To prove: The function expressed as y=2x36x+10 satisfies the given differential equation yxy2y=24x2.

Explanation

Given:

The given function is expressed as y=2x3âˆ’6x+10. The differential equation is given to be âˆ’yâ€´âˆ’xyâ€³âˆ’2yâ€²=âˆ’24x2.

Formula used:

The differentiation formula is ddx(xn)=nxnâˆ’1.

Proof:

Consider the function y=2x3âˆ’6x+10.

Find the first derivative of the function as,

yâ€²=ddx(2x3âˆ’6x+10)=6x2âˆ’6

And, the second derivative of the function as,

yâ€³=d

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