Solving Separable Differential Equations
Read this topicExplanations 5
- This type of differential equation is called "separable" because of the following trick (which will be proven later): dydx=g(x)h(y)dyh(y)=g(x)dx∫dyh(y)=∫g(x)dx\begin{align*} \fr…
By Calvin Lee, Ronald Kwan
- An application/example of this type of differential equation in circuits: Consider a series circuit with a battery (voltage VVV), a capacitor (capacitance CCC), and a resistor (…
By Calvin Lee
- A separable differential equation can be written as a product of a function of xxx and a function of yyy. dydx=g(x)f(y)\frac{dy}{dx}=g(x)f(y)dxdy=g(x)f(y) If f(y)≠0f(y)\neq0f(y…
By Jacky Lee
- We can now examine an application of differential equations in the chemistry of kinetics. Suppose that we are given the differential rate law of a first-order reaction d[A]dt=k[…
By Jacky Lee
- A separable differential equation is an equation of the form dydx=g(x)h(y),\frac{dy}{dx} = g(x)h(y),dxdy=g(x)h(y), where g,hg,hg,h are given functions of x,yx,yx,y, respectivel…
By Victor Wang
Problems 3
- Solve the differential equation dydx=x2y2\frac{dy}{dx}=\frac{x^2}{y^2}dxdy=y2x2 with the initial condition y(0)=2y(0)=2y(0)=2.
- Solve the differential equation dydx=x2y2\frac{dy}{dx}=\frac{x^2}{y^2}dxdy=y2x2 with the initial condition y(0)=2y(0)=2y(0)=2.
- Solve the differential equation ydydx=xe−xy\frac{dy}{dx} = xe^{-x}ydxdy=xe−x for the initial condition y(0)=4y(0) = 4y(0)=4