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# Find a first-order differential equation having the family y2 = Cx as integral curves

Find a first-order differential equation having the family as integral curves.

Since we can differentiate both sides with respect to to get Then, since we have . Substituting this on the right hand side we have the first-order differential equation having the given family as integral curves.

# Find a first-order differential equation having the family xy = C as integral curves

Find a first-order differential equation having the family as integral curves.

Since we can differentiate both sides with respect to to get Thus, the first-order differential equation has the given family as integral curves.

# Find a first-order differential equation having the family x2 – y2 = c as integral curves

Find a first-order differential equation having the family as integral curves.

Since we can differentiate both sides with respect to to get Thus, the first-order differential equation has the given family as integral curves.

# Find a first-order differential equation having the family y = Ce-2x as integral curves

Find a first-order differential equation having the family as integral curves.

Since we can differentiate both sides with respect to to get Then, we plug in our original equation on the right hand side to get the first-order differential equation having the given family as integral curves.

# Find a first-order differential equation having the family 2x + 3y = C as integral curves

Find a first-order differential equation having the family as integral curves.

Since we can differentiate both sides with respect to to get Thus, the first-order differential equation has the given family as integral curves.