In some simple cases the Dirichlet problem can be solved explicitly.

While the model can be solved explicitly it is instructive to analyze the trajectory of the economy in terms of a phase diagram.

Because of its simple structure the equation can be replaced with an equivalent equation with constant coefficients which can then be solved explicitly.

Despite being nonlinear, the model can be solved explicitly, since it is in fact an inhomogeneous linear equation in 1/n.

In some cases, this differential equation (called an equation of motion) may be solved explicitly.

This equation can be solved explicitly.

These ODEs can be solved explicitly in terms of elementary functions, using inverse spectral methods.

Quantum integrable systems can be explicitly solved by Bethe Ansatz or Quantum inverse scattering method.

For example, (3.3) can be easily solved explicitly:

The Schrödinger equation of a spherically-symmetric three-dimensional harmonic oscillator can be solved explicitly by separation of variables, see this article for the present case.