(dy)/(dx)=(15)/(x^(4))*(4y^((3)/(4)))/(3)

Simplify constants and variables: We are given the differential equation: (dy)/(dx) = (15)/(x^(4)) * (4y^((3)/(4)))/(3) First, we need to simplify the right-hand side of the equation by multiplying the constants together and keeping the variables separate.Combine constants and variables: The constants are 15 and 4/3. Multiplying these together gives: 15 * (4/3) = 60/3 = 20 Now we have: (dy)/(dx) = 20 * (1/x^(4)) * y^((3)/(4))Final simplified form: Next, we simplify the expression by combining the terms with the variables x and y: (dy)/(dx) = 20 * x^(-4) * y^((3)/(4)) This is the simplified form of the given differential equation.

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(dy)/(dx)=(15)/(x^(4))*(4y^((3)/(4)))/(3)

$\frac{d y}{d x}=\frac{15}{x^{4}} \cdot \frac{4 y^{\frac{3}{4}}}{3}$

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Algebra 1

Multiplication with rational exponents

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\frac{d y}{d x}=\frac{15}{x^{4}} \cdot \frac{4 y^{\frac{3}{4}}}{3}

Simplify constants and variables: We are given the differential equation: $\newline$ $\frac{dy}{dx} = \frac{15}{x^{4}} \cdot \frac{4y^{\frac{3}{4}}}{3}$ $\newline$ First, we need to simplify the right-hand side of the equation by multiplying the constants together and keeping the variables separate.
Combine constants and variables: The constants are $15$ and $\frac{4}{3}$ . Multiplying these together gives: $\newline$ $15 \times \left(\frac{4}{3}\right) = \frac{60}{3} = 20$ $\newline$ Now we have: $\newline$ $\frac{dy}{dx} = 20 \times \left(\frac{1}{x^{4}}\right) \times y^{\left(\frac{3}{4}\right)}$
Final simplified form: Next, we simplify the expression by combining the terms with the variables $x$ and $y$ : $\frac{dy}{dx} = 20 \cdot x^{-4} \cdot y^{\left(\frac{3}{4}\right)}$ This is the simplified form of the given differential equation.