y×y=y2

1.	y×y=y2
Answer» y² dx = (1 - 3xy) dy dx/dy = 1/(y²) - 3x/y dx/dy + 3x/y = 1/y² This is a first order linear differential equation of the form x' + P(y)x = Q(y) where the integrating factor = e^{(∫P(y) dy)}= e^{(∫3/y dy)} = y³ Multiplying both sides by integrating factor: y³(dx/dy) + 3y^2x = y Note that the left hand side equals d/dy[x*y^3], so: d/dy[xy³] = y Integrating both sides: xy³ = (y²)/2 + C x = 1/(2y) + C/(y³)

Answer»

y² dx = (1 - 3xy) dy

dx/dy = 1/(y²) - 3x/y

dx/dy + 3x/y = 1/y²

This is a first order linear differential equation of the form x' + P(y)x = Q(y) where the integrating factor = e^{(∫P(y) dy)}= e^{(∫3/y dy)} = y³

Multiplying both sides by integrating factor:

y³(dx/dy) + 3y^2x = y

Note that the left hand side equals d/dy[x*y^3], so: d/dy[xy³] = y

Integrating both sides:

xy³ = (y²)/2 + C

x = 1/(2y) + C/(y³)

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y×y=y2

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