Question

Solve:(5x+6y)dx+(8y^3-6x)dy=0.

Answer 1

The equation is ( 5x + 6y) dx + ( 8y^3 - 6x) dy = 0.

Simplify the equation .

( 5x + 6y)  * dx + ( 8y^3 - 6x)  * dy = 0

Reorder the terms for multiplication.

dx (5x + 6y) + ( 8y^3 - 6x)  * dy = 0

( 5x * dx + 6y * dx ) + ( 8y^3 - 6x)  * dy = 0

Reorder the terms.

( 5dx^2 + 6dxy ) + ( 8y^3 - 6x)  * dy = 0

Reorder the terms for multiplication.

( 5dx^2 + 6dxy ) + ( 8y^3 * dy - 6x * dy ) = 0

( 5dx^2 + 6dxy ) + ( 8dy^4 - 6dxy ) = 0

( 5dx^2 + 6dxy ) + ( 8dy^4 - 6dxy ) = 0

Reorder the terms.

8dy^4 + 5dx^2 + 6dxy - 6dxy = 0

Combine like terms : 6dxy - 6dxy = 0.

8dy^4 + 5dx^2 = 0

d(8y^4 + 5x^2) = 0.

Apply zero product property.

d = 0             and         8y^4 + 5x^2 = 0

Therefore, the solution to 8y^4 + 5x^2 = 0 could not be determined, and the solution of d = { 0 }.

Comments

Solution is wrong .You should use application of derivatives