Solve the equation. (dy)/(dx)=(x^(2))/(10 y)-(2x)/(5y) Choose 1 answer: (A) y=+-sqrt((x^(3))/(15)-(2x^(2))/(5)+C) (B) y=+-sqrt((x^(3))/(15)-(2x^(2))/(5))+C (C) y=Ce^((10x^(3))/(3)-20x^(2)) (D) y=+-e^((10x^(3))/(3)-20x^(2))+C

Combine terms over common denominator: We are given the differential equation: (dy)/(dx) = (x^2)/(10y) - (2x)/(5y) To solve this, we will first combine the terms on the right-hand side over a common denominator.Separate variables and multiply: Now, we will separate variables by multiplying both sides by y and dx, and dividing by -3x^2. y dy = (-1/3) x^2 dxIntegrate both sides: Next, we integrate both sides of the equation. ∫ y dy = ∫ (-1/3) x^2 dx (1/2)y^2 = (-1/9)x^3 + CSolve for y: Now, we solve for y by taking the square root of both sides. y = ±sqrt((2/9)x^3 + 2C)

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Solve the equation.

(dy)/(dx)=(x^(2))/(10 y)-(2x)/(5y)
Choose 1 answer:
(A)
y=+-sqrt((x^(3))/(15)-(2x^(2))/(5)+C)
(B)
y=+-sqrt((x^(3))/(15)-(2x^(2))/(5))+C
(C)
y=Ce^((10x^(3))/(3)-20x^(2))
(D)
y=+-e^((10x^(3))/(3)-20x^(2))+C

Solve the equation. $\newline$ $\frac{d y}{d x}=\frac{x^{2}}{10 y}-\frac{2 x}{5 y}$ $\newline$ Choose $1$ answer: $\newline$ (A) $y= \pm \sqrt{\frac{x^{3}}{15}-\frac{2 x^{2}}{5}+C}$ $\newline$ (B) $y= \pm \sqrt{\frac{x^{3}}{15}-\frac{2 x^{2}}{5}}+C$ $\newline$ (C) $y=C e^{\frac{10 x^{3}}{3}-20 x^{2}}$ $\newline$ (D) $y= \pm e^{\frac{10 x^{3}}{3}-20 x^{2}}+C$

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Calculus

Find derivatives of using multiple formulae

Full solution

Q. Solve the equation.

\newline

\frac{d y}{d x}=\frac{x^{2}}{10 y}-\frac{2 x}{5 y}

\newline

Choose

1

answer:

\newline

(A)

y= \pm \sqrt{\frac{x^{3}}{15}-\frac{2 x^{2}}{5}+C}

\newline

(B)

y= \pm \sqrt{\frac{x^{3}}{15}-\frac{2 x^{2}}{5}}+C

\newline

(C)

y=C e^{\frac{10 x^{3}}{3}-20 x^{2}}

\newline

(D)

y= \pm e^{\frac{10 x^{3}}{3}-20 x^{2}}+C

Combine terms over common denominator: We are given the differential equation: $\newline$ $(\frac{dy}{dx}) = \frac{x^2}{10y} - \frac{2x}{5y}$ $\newline$ To solve this, we will first combine the terms on the right-hand side over a common denominator.
Separate variables and multiply: Now, we will separate variables by multiplying both sides by $y$ and $dx$ , and dividing by $-3x^2$ . $y \, dy = \left(-\frac{1}{3}\right) x^2 \, dx$
Integrate both sides: Next, we integrate both sides of the equation. $\newline$ $\int y \, dy = \int (-\frac{1}{3}) x^2 \, dx$ $\newline$ $\frac{1}{2}y^2 = (-\frac{1}{9})x^3 + C$
Solve for y: Now, we solve for y by taking the square root of both sides. $\newline$ $y = \pm\sqrt{\left(\frac{2}{9}\right)x^3 + 2C}$