- #1

JSGhost

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## Homework Statement

Solve the following differential equation

8x - 2y sqrt(x^2 + 1) dy/dx = 0

subject to the initial condition: y(0) = -3.

y = ?

## Homework Equations

Separable DE's

dy/dx = g(x)/f(y)

## The Attempt at a Solution

8x - 2y sqrt(x^2 + 1) dy/dx = 0

8x = 2y sqrt(x^2 + 1) dy/dx

[8x/sqrt(x^2+1)]dx = 2y dy

integrate both sides

u = x^2 + 1

du = 2x dx

4 (integral) [1/sqrt(u)] du = y^2

4(2u^(1/2)) + c = y^2

8 sqrt(x^2+1) + c = y^2

Since y(0) = -3.

Substitute to find c.

8sqrt((0)^2+1) + c = (-3)^2

8 + c = 9

c = 1

y^2 = 8 sqrt(x^2+1) + 1

I get that answer but it isn't correct. I am using webwork and need help solving the equation. Thanks.