How to solve the differential equation: \((x^2\cos x – y)dx + xdy = 0\)
Question: Solve \((x^2\cos x – y)dx + xdy = 0\). Answer: Rewrite the equation as follows: \[ \frac{dy}{dx}-\frac{y}{x}=-x\cos x \] […]
Tag: differential equation
Solve the differential equation: \(x\frac{dy}{dx}+y=x\ln x\)
Question: (1) Solve \(x\frac{dy}{dx}+y=0\) (2) Solve \(x\frac{dy}{dx}+y=x\ln x\) by using the result from (1). Answer: (1) The original differential equation […]
Solve the differential equation, \(\frac{dy}{dx}+P(x)y=Q(x)\).
Question: (1) Find the general solution of \(\frac{dy}{dx}+P(x)y=Q(x)\), where \(P(x)\) and \(Q(x)\) are functions of \(x\). (2) Solve the following […]
Damped oscillation of a spring motion: Linear differential equation
Question: A 0.400-kg bob is attached to a spring of its force constant \(k=200\) N/m and this motion is subject […]
The bounded solution of a first order ordinary differential equation
Question: Find the bounded solution of the following ordinary differential equation: \[ \frac{dx}{dt} = 2x + \sin t \] for \(-\infty […]