91Ó°ÊÓ

In Problems 1-40 find the general solution of the given differential equation. State an interval on which the general solution is defined. $$ \frac{d y}{d x}+y=e^{3 x} $$

Classify each differential equation as separable, exact, linear, homogeneous, or Bernoulli. Some equations may be more than one kind. Do not solve the equations. $$\frac{d y}{d x}=\frac{y^{2}+y}{x^{2}+x}$$

In Problems 1-24 determine whether the given equation is exact. If it is exact, solve it. $$ \left(2 y^{2} x-3\right) d x+\left(2 y x^{2}+4\right) d y=0 $$

Solve the given homogeneous equation by using an appropriate substitution. $$ \left(y^{2}+y x\right) d x-x^{2} d y=0 $$

Solve the given differential equation by separation of variables. $$ e^{x} \frac{d y}{d x}=2 x $$

In Problems 1-24 determine whether the given equation is exact. If it is exact, solve it. $$ \left(2 y-\frac{1}{x}+\cos 3 x\right) \frac{d y}{d x}+\frac{y}{x^{2}}-4 x^{3}+3 y \sin 3 x=0 $$

Classify each differential equation as separable, exact, linear, homogeneous, or Bernoulli. Some equations may be more than one kind. Do not solve the equations. $$\frac{d y}{d x}=5 y+y^{2}$$

In Problems 1-40 find the general solution of the given differential equation. State an interval on which the general solution is defined. $$ \frac{d y}{d x}=y+e^{x} $$

Solve the given homogeneous equation by using an appropriate substitution. $$ \left(y^{2}+y x\right) d x+x^{2} d y=0 $$

In Problems 1-24 determine whether the given equation is exact. If it is exact, solve it. $$ (x+y)(x-y) d x+x(x-2 y) d y=0 $$