Differential Equations

Let $f(x)$ be differentiable s.t. $f^{\prime }(x)=2-f(x)/x$ and $f(1)=1$. Then $f(x)$ is:

The solution of the differential equation $dy/dx+y/x=x^2$ is:

A cup of coffee cools according to Newton's law so that \frac{dT}{dt} = -k(T - T_s); identify the co...

Solve the repeated-root equation \frac{d^2y}{dx^2} - 6\frac{dy}{dx} + 9y = 0 and state the general s...

The length of the subtangent at any point of a curve is constant and equal to a, leading to a differ...

Solve the differential equation \frac{dy}{dx} = e^{x-y} and express the general solution relating th...

The family of curves y = Cx^2 has orthogonal trajectories that we must determine by replacing the sl...

Find the general solution of the second-order constant-coefficient equation \frac{d^2y}{dx^2} - 5\fr...

A population grows so that its rate of change is proportional to its current size, modeled by \frac{...

Consider the equation x\frac{dy}{dx} + 2y = x^2 with x positive, and identify the general solution a...

At every point on a curve the slope equals the ratio of the y-coordinate to the x-coordinate, and we...

Determine the general solution of the equation \frac{d^2y}{dx^2} + 4y = 0 whose auxiliary equation p...