second-order equation

Since this is a second-order equation, two such conditions are necessary to determine these values.

In particular, Nyström methods work directly with second-order equations.

Recognise different types of complementary function for second-order equations: oscillating, critical and purely decaying behaviour.

If a decomposition of type , or has been obtained for a second-order equation , a fundamental system may be given explicitly.

With the intention of demonstrating them, Torres also built a machine for solving a second-order equation with complex coefficients, and an integrator.

For the second-order equations, they can be considered as governing equations using to describe the motion of fluid with mass source and force source .

Then, integrate to find the full solution of the original non-homogeneous second-order equation, exhibiting two constants of integration as it should:

The Renner equations for the bending vibrations of linear molecules are derived from the second-order equation of the APT.

Hamilton's equations consist of 2n first-order differential equations, while Lagrange's equations consist of n second-order equations.

The most common Cauchy-Euler equation is the second-order equation, appearing in a number of physics and engineering applications, such as when solving Laplace's equation in polar coordinates.

Also as before, this stacked equation and thus the original second-order equation are stable if and only if all eigenvalues of the matrix L are smaller than unity in absolute value.

Canonical forms for second-order linear equations with constant coefficients, classification of linear second-order equations, method of separation of variables, first-order PDE's, method of characteristics.

For comparison, in the equivalent Euler-Lagrange equations of motion of Lagrangian mechanics, the conjugate momenta also do not appear; however, those equations are a system of N, generally second-order equations for the time evolution of the generalized coordinates.

In fact more is true: Schwarz's list underlies all second-order equations with regular singularities on compact Riemann surfaces having finite monodromy, by a pullback from the hypergeometric equation on the Riemann sphere by a complex analytic mapping, of degree computable from the equation's data.