# Differential equations Answers

Differential equations

### $$\displaystyle{\frac{{{\left.{d}{y}\right.}}}{{{\left.{d}{x}\right.}}}}={\frac{{{x}{y}+{3}{x}-{y}-{3}}}{{{x}{y}-{2}{x}+{4}{y}-{8}}}}$$ Solve it using variable separation

Differential equations

### Population y grows according to the equation dy/dt = ky, where is a constant and t is measured in years. Of the population doubles every ten years, then the value of k is ?

Differential equations

### The problem question is: $$\displaystyle{\frac{{{\left.{d}{y}\right.}}}{{{\left.{d}{t}\right.}}}}={a}{y}+{b}{y}^{{2}}$$ we have to sketch the graph f(y) versus y, determine the critical points, and classify each one as asymptotically stable or unstable.Thing is, how do you get the critical points?

Differential equations

### solve the initial value problem: $$\displaystyle{\left({\tan{{\left({y}\right)}}}-{2}\right)}{\left.{d}{x}\right.}+{\left({x}{{\sec}^{{2}}{\left({y}\right)}}+\frac{{1}}{{y}}\right)}{\left.{d}{y}\right.}={0}$$, y(0)=1

Differential equations

### Find dw/dt using the appropriate Chain Rule. Evaluate $$\frac{dw}{dt}$$ at the given value of t. Function: $$w=x\sin y,\ x=e^t,\ y=\pi-t$$ Value: t = 0

Differential equations