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1) Use a substitution to solve the following differential equation.

dy

dx = 3x + y + 9x

2 + 6xy + y

2 − 15

2) Use a substitution to solve the following differential equation.

dx

dt +

x

t

= 3x

3

3) Use a substitution to solve the following differential equation.

xy0 = xe−y/x + y x > 0

4) Solve the following ”almost exact” differential equation by first finding

an integrating factor.

(2xy3 + y

4

)dx + (xy3 − 2)dy