Determine whether the given function is a solution to the given differential equation.\ y = cos x + x^6, quad frac{d^2y}{dx^2} + y = x^6 + 30x^4

Name: Determine whether the given function is a solution to the given differential equation.y = cos x + x^6, quad fracd^2ydx^2 + y = x^6 + 30x^4
Uploaded: 2023-02-23T10:17:48-08:00
Duration: 3 min 1 s
Channel: Madhur L
Description: Determine whether the given function is a solution to the given differential equation.y = cos x + x^6, quad fracd^2ydx^2 + y = x^6 + 30x^4

          Determine whether the given function is a solution to the given differential equation.\
y = cos x + x^6, quad frac{d^2y}{dx^2} + y = x^6 + 30x^4

$Determine whether the given function is a solution to the given differential equation.y = cos x + x^6, quad fracd^2ydx^2 + y = x^6 + 30x^4$

Added by Cory M.

Calculus: Early Transcendentals

James Stewart 8th Edition

Instant Answer

Solved by Expert Madhur L

02/23/2023

Step 1

Y = cos(x) + x^6 dY/dx = -sin(x) + 6x^5 Now, let's plug this derivative and the function Y into the given differential equation and see if it holds true. y = x^6 + 30x * dx dY/dx = 6x^5 - sin(x) Plugging in Y and dY/dx into the equation: x^6 + 30x * (-sin(x) Show more…

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