First Order Differential Equations
Using Newton's second law of motion (mass \(\times\) acceleration = net force applied), set up an ordinary differential equation for \(v(t).\)
Let \(k\) denote the drag coefficient.
by
Lawahar Qasid
by
Michael Lee
You are given the differential equation \( \frac{dy}{dx} + y \ln x = x^{-x} e^{-x} \) and the initial condition \( y(1) = 0 \)
If the value of \( y(2) \) can be written in the form \( \dfrac{e^{2}+a}{be^2} \) determine the value of \( a + b \).
by
Cole Coupland
Solve the ODE \[xy'+y={(xy)}^{2} \ln{x}\] where \(y(1)=\frac{1}{3}\). Calculate the value of \(y(e)\) to 3 decimal places.
by
Steven Zheng
What is the order of the differential equation \[x^2.\left( \dfrac{d^2y}{dx^2} \right)^6+y^{\frac{-2}{3}}.\sqrt{1+\left( \dfrac{d^3y}{dx^3} \right)^5}+\dfrac{d^2}{dx^2}. \left( \dfrac{d^2y}{dx^2} \right)^{\frac{-2}{3}} =0?\]
by
Sandeep Bhardwaj