An autonomous ODE has equilibria at \(P=5\) (unstable) and \… An autonomous ODE has equilibria at \(P=5\) (unstable) and \(P=10\) (stable). If \(P(0)=7\), what does P(t) tend to as \(t\to\infty\)? Read Details
The Embargo Act of 1806 by Jefferson was most criticized by… The Embargo Act of 1806 by Jefferson was most criticized by the Federalists Read Details
Solve \(\frac{dv}{dt}=\frac{4t}{2v}\) where \(v(0)=-3\) Solve \(\frac{dv}{dt}=\frac{4t}{2v}\) where \(v(0)=-3\) Read Details
The acceleration of a particle equals the negative of its po… The acceleration of a particle equals the negative of its position x(t). Write the ODE for x(t). Read Details
Consider \(y’=2(y-1)^2\). After separation of variables we g… Consider \(y’=2(y-1)^2\). After separation of variables we get the solutions \(y=1-\frac{{1}}{{2x+C}}\). Find the solution satisfying \(y(0)=1\). Read Details
An autonomous ODE has equilibria at \(P=5\) (unstable) and \… An autonomous ODE has equilibria at \(P=5\) (unstable) and \(P=10\) (stable). If \(P(0)=10\), what is P(t)? Read Details
Goal: solve \(y’+\frac{{2}}{{x}}y=x\). Integrating factor \(… Goal: solve \(y’+\frac{{2}}{{x}}y=x\). Integrating factor \(\rho=x^2\) gives: $$(x^2y)’=x^3$$ After integrating we get \(x^2y=\frac{{x^4}}{{4}}+C\). What is the correct solution for y? Read Details
A population has P(0)=8 and \(P(t)=\frac{{40}}{{8-3e^{{5t}}}… A population has P(0)=8 and \(P(t)=\frac{{40}}{{8-3e^{{5t}}}}\). What happens to P(t) as t increases? Read Details
The graph of y(x) has the property that the tangent line at… The graph of y(x) has the property that the tangent line at any point (x, y) passes through the point (0, 3). Write an ODE for y(x). Read Details
A student finds the general solution to \(\frac{dy}{dx}=\fra… A student finds the general solution to \(\frac{dy}{dx}=\frac{{1}}{{x+3}}\) and gives \(y=\ln|x+3|+C\). What is the issue? Read Details