Search Results for ""

The solution to the differential equation [D^(2v)+alphaD^v+betaD^0]y(t)=0 (1) is y(t)={e_alpha(t)-e_beta(t) for alpha!=beta; ...

The second-order ordinary differential equation (Moon and Spencer 1961, p. 157; Zwillinger 1997, p. 166).

The second-order ordinary differential equation y^('')+k/xy^'+epsilony^'y=0.

The second-order ordinary differential equation y^('')+f(x)y^'+y=0.

The ordinary differential equation y^'=-y(1+kappa(x)y)/(1-kappa(x)y).

A universal differential equation (UDE) is a nontrivial differential-algebraic equation with the property that its solutions approximate to arbitrary accuracy any continuous ...

The ordinary differential equation y^('')+r/zy^'=(Az^m+s/(z^2))y. (1) It has solution y=c_1I_(-nu)((2sqrt(A)z^(m/2+1))/(m+2))z^((1-r)/2) ...

A generalization of the Bessel differential equation for functions of order 0, given by zy^('')+y^'+(z+A)y=0. Solutions are y=e^(+/-iz)_1F_1(1/2∓1/2iA;1;∓2iz), where ...

The second-order ordinary differential equation (d^2y)/(dx^2)+[theta_0+2sum_(n=1)^inftytheta_ncos(2nx)]y=0, (1) where theta_n are fixed constants. A general solution can be ...

A differential ideal is an ideal I in the ring of smooth forms on a manifold M. That is, it is closed under addition, scalar multiplication, and wedge product with an ...