Question

6. Find the integrating factor and solve DE. (1 Point) (xy + 1) dx + x (x + 4y - 2) dy = 0 ln x + xy + 2y (y - 1) = c ln x + 2xy + 2y (y - 1) = c ln x^2 + xy + 2y (y - 1) = c ln x + xy + 2y (y - 1) = cx 7. Linear DE: Solve the ff (1 Point) dy/dx + 2y/x = x^4 y = x^5 + c/x^2 xy = x^5 + c/x^2 y = x^5 + x^2 + c y = x^5 + cx^2

          6. Find the integrating factor and solve DE.
(1 Point)
(xy + 1) dx + x (x + 4y - 2) dy = 0
ln x + xy + 2y (y - 1) = c
ln x + 2xy + 2y (y - 1) = c
ln x^2 + xy + 2y (y - 1) = c
ln x + xy + 2y (y - 1) = cx
7. Linear DE: Solve the ff
(1 Point)
dy/dx + 2y/x = x^4
y = x^5 + c/x^2
xy = x^5 + c/x^2
y = x^5 + x^2 + c
y = x^5 + cx^2

6. Find the integrating factor and solve DE.
(1 Point)
(xy + 1) dx + x (x + 4y - 2) dy = 0
ln x + xy + 2y (y - 1) = c
ln x + 2xy + 2y (y - 1) = c
ln x^2 + xy + 2y (y - 1) = c
ln x + xy + 2y (y - 1) = cx
7. Linear DE: Solve the ff
(1 Point)
dy/dx + 2y/x = x^4
y = x^5 + c/x^2
xy = x^5 + c/x^2
y = x^5 + x^2 + c
y = x^5 + cx^2

Added by Tasha H.

Calculus: Early Transcendentals

James Stewart 8th Edition

Instant Answer

Solved by Expert Sri K

10/03/2023

Step 1

First, we rewrite the given differential equation in the standard form: (xy + 1) dx + x(x + 4y - 2) dy = 0 Divide by x(x + 4y - 2): (1 + \frac{1}{x}) dx + (1 + \frac{4y}{x} - \frac{2}{x}) dy = 0 Now, we can see that this is a first-order linear differential Show more…

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Find the integrating factor and solve the differential equation: (xy + 1) dx + x (x + 4y - 2) dy = 0 Inx + xy + 2y (y - 1) = c Inx + 2xy + 2y (y - 1) = c Inx^2 + xy + 2y (y - 1) = c Inx + xy + 2y (y - 1) = cx Linear DE: Solve the following dy/dx + 2y/x = x^4 y = x^5 + c/x^2 xy = x^5 + c/x^2 y = x^5 + x^2 + c y = x^5 + cx^2