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Magazine Problem 7
Solve the given homogeneous equation by using an appropriate substitution. $$ \frac{d y}{d x}=\frac{y-x}{y+x} $$
Problem 7
In Problems 1-40 find the general solution of the given differential equation. State an interval on which the general solution is defined. $$ y^{\prime}+3 x^{2} y=x^{2} $$
Problem 7
Classify each differential equation as separable, exact, linear, homogeneous, or Bernoulli. Some equations may be more than one kind. Do not solve the equations. $$y d x=\left(y-x y^{2}\right) d y$$
Problem 7
Solve the given differential equation by separation of variables. $$ x y^{\prime}=4 y $$
Problem 8
Solve the given differential equation by separation of variables. $$ \frac{d y}{d x}+2 x y=0 $$
Problem 8
Classify each differential equation as separable, exact, linear, homogeneous, or Bernoulli. Some equations may be more than one kind. Do not solve the equations. $$x \frac{d y}{d x}=y e^{v y}-x$$
Problem 8
In Problems 1-40 find the general solution of the given differential equation. State an interval on which the general solution is defined. $$ y^{\prime}+2 x y=x^{3} $$
Problem 8
Solve the given homogeneous equation by using an appropriate substitution. $$ \frac{d y}{d x}=\frac{x+3 y}{3 x+y} $$
Problem 9
In Problems 1-40 find the general solution of the given differential equation. State an interval on which the general solution is defined. $$ x^{2} y^{\prime}+x y=1 $$
Problem 9
Solve the given differential equation by separation of variables. $$ \frac{d y}{d x}=\frac{y^{3}}{x^{2}} $$
