(x+1)dy=5x^2(x+1)dx-y

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Solution for (x+1)dy=5x^2(x+1)dx-y equation:


Simplifying
(x + 1) * dy = 5x2(x + 1) * dx + -1y

Reorder the terms:
(1 + x) * dy = 5x2(x + 1) * dx + -1y

Reorder the terms for easier multiplication:
dy(1 + x) = 5x2(x + 1) * dx + -1y
(1 * dy + x * dy) = 5x2(x + 1) * dx + -1y

Reorder the terms:
(dxy + 1dy) = 5x2(x + 1) * dx + -1y
(dxy + 1dy) = 5x2(x + 1) * dx + -1y

Reorder the terms:
dxy + 1dy = 5x2(1 + x) * dx + -1y

Reorder the terms for easier multiplication:
dxy + 1dy = 5x2 * dx(1 + x) + -1y

Multiply x2 * dx
dxy + 1dy = 5dx3(1 + x) + -1y
dxy + 1dy = (1 * 5dx3 + x * 5dx3) + -1y
dxy + 1dy = (5dx3 + 5dx4) + -1y

Solving
dxy + 1dy = 5dx3 + 5dx4 + -1y

Solving for variable 'd'.

Move all terms containing d to the left, all other terms to the right.

Add '-5dx3' to each side of the equation.
dxy + -5dx3 + 1dy = 5dx3 + 5dx4 + -5dx3 + -1y

Reorder the terms:
dxy + -5dx3 + 1dy = 5dx3 + -5dx3 + 5dx4 + -1y

Combine like terms: 5dx3 + -5dx3 = 0
dxy + -5dx3 + 1dy = 0 + 5dx4 + -1y
dxy + -5dx3 + 1dy = 5dx4 + -1y

Add '-5dx4' to each side of the equation.
dxy + -5dx3 + -5dx4 + 1dy = 5dx4 + -5dx4 + -1y

Combine like terms: 5dx4 + -5dx4 = 0
dxy + -5dx3 + -5dx4 + 1dy = 0 + -1y
dxy + -5dx3 + -5dx4 + 1dy = -1y

Combine like terms: -1y + y = 0
dxy + -5dx3 + -5dx4 + 1dy + y = 0

The solution to this equation could not be determined.

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