Mathematics: Which of the following functions are solutions of the differential equation y + y = 3 sin x? (select all that apply) a. y=3sinx b. y=3xsinx-5xcosx c. y=-3/2xcosx d. y=3cosx e. y=3/2xsinx

Which of the following functions are solutions of

Ответ:

oliup567

14.01.2022

Step-by-step explanation:

We must compute the derivatives and check if the equation is satisfied.

A. $y'=(3\sin x)'=3\cos x$ . Differentiate again to get $y''=(3\cos x)'=-3\sin x$ , then $y''+y=-3\sin x+3\sin x=0\neq 3\sin x$ so this choice of y doesn't solve the equation.

B. $y'=3\sin x+3x\cos x-5\cosx +5x\sin x=(5x+3)\sin x+(3x-5)\cos x$ and $y''=5\sin x+(5x+3)\cos x+3\cos x-(3x-5)\sin x=(10-3x)\sin x+(5x+6)\cos x$ , then $y''+y=10\sin x+6\cos x\neq 3\sin x$ so y is not a solution

C. $y'=\frac{-3}{2}\cos x+\frac{3}{2}x\sin x$ hence $y''=\frac{3}{2}\sin x+\frac{3}{2}\sin x+\frac{3}{2}x\cos x=3\sin x+\frac{3}{2}x\cos x$ . Then $y''+y=3\sin x+\frac{3}{2}x\cos x-\frac{3}{2}x\cos x=3\sin x$ so y is a solution.

D. $y'=-3\sin x$ and $y''=-3\cos x$ , then y''+y=0 thus y isn't a solution

E. $y'=\frac{3}{2}\sin x+\frac{3}{2}x\cos x$ hence $y''=\frac{3}{2}\cos x+\frac{3}{2}\cos x-\frac{3}{2}x\sin x=3\cos x-\frac{3}{2}x\cos x$ . Then $y''+y=3\cos x-\frac{3}{2}x\cos x-\frac{3}{2}x\cos x=3\cos x\neq 3\sin x$ then y is not a solution.

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Ответ:

dessyrob05

01.04.2020

Mathematics

Step-by-step explanation:

In this problem, we need o find the rate in cups of lime juice per cup of yogurt.

It is given that, a salad dressing recipe includes 4/5 cup of lime juice for every 2 cups of Greek yogurt. Its rate is given by :

$R=\dfrac{\dfrac{4}{5}\ \text{cups of lime juice}}{2\ \text{cups}}\\\\R=\dfrac{4}{5}\times 2\\\\R=\dfrac{8}{5}\ \text{cups of lime juice per cup}$

Hence, the rate is 8/5 cups of lime juice per cup.

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Which of the following functions are solutions of the differential equation y'' + y = 3 sin x? (select all that apply)

a. y=3sinx
b. y=3xsinx-5xcosx
c. y=-3/2xcosx
d. y=3cosx
e. y=3/2xsinx

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Which of the following functions are solutions of the differential equation y'' + y = 3 sin x? (select all that apply) a. y=3sinx b. y=3xsinx-5xcosx c. y=-3/2xcosx d. y=3cosx e. y=3/2xsinx

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Which of the following functions are solutions of the differential equation y'' + y = 3 sin x? (select all that apply)

a. y=3sinx
b. y=3xsinx-5xcosx
c. y=-3/2xcosx
d. y=3cosx
e. y=3/2xsinx