Solve the equation. (dy)/(dx)=((xy)^(2))/(8)+y^(2) Choose 1 answer: (A) y=-(x^(2)+16)/(16+C) (B) y=-(16)/(x^(2)+16+C) (c) y=-(x^(3)+24 x)/(24+C) (D) y=-(24)/(x^(3)+24 x+C)

Recognize type of DE: Recognize the type of differential equation. This is a first-order non-linear differential equation.Attempt separation of variables: Attempt separation of variables. Assuming y ≠ 0, divide both sides by y^2: (dy/y^2) = (x^2y^2)/(8y^2) + 1 (dy/y^2) = (x^2)/(8) + 1

Resources

Testimonials

Plans

Resources

Testimonials

Plans

AI tutor

Welcome to Bytelearn!

Let’s check out your problem:

Solve the equation.

(dy)/(dx)=((xy)^(2))/(8)+y^(2)
Choose 1 answer:
(A)
y=-(x^(2)+16)/(16+C)
(B)
y=-(16)/(x^(2)+16+C)
(c)
y=-(x^(3)+24 x)/(24+C)
(D)
y=-(24)/(x^(3)+24 x+C)

Solve the equation. $\newline$ $\frac{d y}{d x}=\frac{(x y)^{2}}{8}+y^{2}$ $\newline$ Choose $1$ answer: $\newline$ (A) $y=-\frac{x^{2}+16}{16+C}$ $\newline$ (B) $y=-\frac{16}{x^{2}+16+C}$ $\newline$ (c) $y=-\frac{x^{3}+24 x}{24+C}$ $\newline$ (D) $y=-\frac{24}{x^{3}+24 x+C}$

View step-by-step help

Home

Math Problems

Calculus

Find derivatives of using multiple formulae

Full solution

Q. Solve the equation.

\newline

\frac{d y}{d x}=\frac{(x y)^{2}}{8}+y^{2}

\newline

Choose

1

answer:

\newline

(A)

y=-\frac{x^{2}+16}{16+C}

\newline

(B)

y=-\frac{16}{x^{2}+16+C}

\newline

(c)

y=-\frac{x^{3}+24 x}{24+C}

\newline

(D)

y=-\frac{24}{x^{3}+24 x+C}

Recognize type of DE: Recognize the type of differential equation. $\newline$ This is a first-order non-linear differential equation.
Attempt separation of variables: Attempt separation of variables. $\newline$ Assuming $y \neq 0$ , divide both sides by $y^2$ : $\newline$ $\frac{dy}{y^2} = \frac{x^2y^2}{8y^2} + 1$ $\newline$ $\frac{dy}{y^2} = \frac{x^2}{8} + 1$