(dy)/(dx)=(5y)/(x) Is y=-2x^(5) a solution to the above equation? Choose 1 answer: (A) Yes (B) No

Differentiate y: To determine if y = -2x^5 is a solution to the differential equation (dy)/(dx) = (5y)/(x), we need to differentiate y with respect to x and then substitute the result into the differential equation to see if it holds true. Let's differentiate y = -2x^5 with respect to x. (dy)/(dx) = d(-2x^5)/dx (dy)/(dx) = -2 * 5x^(5-1) (dy)/(dx) = -10x^4Substitute into equation: Now we substitute y = -2x^5 into the right side of the differential equation (5y)/(x) to see if it equals the derivative we found. (5y)/(x) = 5(-2x^5)/x (5y)/(x) = -10x^4Compare derivative and equation: We compare the derivative (dy)/(dx) = -10x^4 with the expression we found by substituting y into the differential equation, which is also -10x^4. Since both sides are equal, y = -2x^5 is indeed a solution to the differential equation (dy)/(dx) = (5y)/(x).

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(dy)/(dx)=(5y)/(x)
Is
y=-2x^(5) a solution to the above equation?
Choose 1 answer:
(A) Yes
(B)
No

$\frac{d y}{d x}=\frac{5 y}{x}$ $\newline$ Is $y=-2 x^{5}$ a solution to the above equation? $\newline$ Choose $1$ answer: $\newline$ (A) Yes $\newline$ (B) $\mathrm{No}$

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Math Problems

Grade 8

Is (x, y) a solution to the nonlinear equation?

Full solution

\frac{d y}{d x}=\frac{5 y}{x}

\newline

y=-2 x^{5}

a solution to the above equation?

\newline

Choose

1

answer:

\newline

(A) Yes

\newline

(B)

\mathrm{No}

Differentiate $y$ : To determine if $y = -2x^5$ is a solution to the differential equation $\frac{dy}{dx} = \frac{5y}{x}$ , we need to differentiate $y$ with respect to $x$ and then substitute the result into the differential equation to see if it holds true. $\newline$ Let's differentiate $y = -2x^5$ with respect to $x$ . $\newline$ $\frac{dy}{dx} = \frac{d(-2x^5)}{dx}$ $\newline$ $\frac{dy}{dx} = -2 \cdot 5x^{5-1}$ $\newline$ $\frac{dy}{dx} = -10x^4$
Substitute into equation: Now we substitute $y = -2x^5$ into the right side of the differential equation $\frac{5y}{x}$ to see if it equals the derivative we found. $\newline$ $\frac{5y}{x} = \frac{5(-2x^5)}{x}$ $\newline$ $\frac{5y}{x} = -10x^4$
Compare derivative and equation: We compare the derivative $\frac{dy}{dx} = -10x^4$ with the expression we found by substituting $y$ into the differential equation, which is also $-10x^4$ . Since both sides are equal, $y = -2x^5$ is indeed a solution to the differential equation $\frac{dy}{dx} = \frac{5y}{x}$ .