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To solve the heat conduction equation on a two-dimensional disk of radius a=1, try to separate the equation using U(r,theta,t)=R(r)Theta(theta)T(t). (1) Writing the theta and ...

On the surface of a sphere, attempt separation of variables in spherical coordinates by writing F(theta,phi)=Theta(theta)Phi(phi), (1) then the Helmholtz differential ...

The second-order ordinary differential equation (d^2y)/(dx^2)-2x(dy)/(dx)+lambday=0. (1) This differential equation has an irregular singularity at infty. It can be solved ...

A homogeneous linear ordinary differential equation with constant coefficients is an ordinary differential equation in which coefficients are constants (i.e., not functions), ...

An inhomogeneous linear ordinary differential equation with constant coefficients is an ordinary differential equation in which coefficients are constants (i.e., not ...

A particular solution to a differential equation corresponding to a specific value of the equation's free parameters. For example, the integral curves of the differential ...

An integrating factor is a function by which an ordinary differential equation can be multiplied in order to make it integrable. For example, a linear first-order ordinary ...

Consider a second-order ordinary differential equation y^('')+P(x)y^'+Q(x)y=0. If P(x) and Q(x) remain finite at x=x_0, then x_0 is called an ordinary point. If either P(x) ...

A procedure for determining the behavior of an nth order ordinary differential equation at a removable singularity without actually solving the equation. Consider ...

Overdamped simple harmonic motion is a special case of damped simple harmonic motion x^..+betax^.+omega_0^2x=0, (1) in which beta^2-4omega_0^2>0. (2) Therefore ...