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The ordinary differential equation y^('')+k/xy^'+deltae^y=0.

The solution u(x,y)=int_0^xdxiint_1^yR(xi,eta;x,y)f(xi,eta)deta, where R(x,y;xieta) is the Riemann function of the linear Goursat problem with characteristics phi=psi=0 ...

For the Helmholtz differential equation to be separable in a coordinate system, the scale factors h_i in the Laplacian del ...

The second-order ordinary differential equation y^('')-[(M^2-1/4+K^2-2MKcosx)/(sin^2x)+(sigma+K^2+1/4)]y=0.

The partial differential equation u_(xx)=au_(tt)+bu_t+cu.

The second-order ordinary differential equation y^('')=y^(3/2)x^(-1/2).

Solution of a system of second-order homogeneous ordinary differential equations with constant coefficients of the form (d^2x)/(dt^2)+bx=0, where b is a positive definite ...

The ordinary differential equation y^('')+1/2[1/(x-a_1)+1/(x-a_2)+1/(x-a_3)]y^' +1/4[(A_0+A_1x+A_2x^2)/((x-a_1)(x-a_2)(x-a_3))]y=0.

The second-order ordinary differential equation y^('')+[A+Bcos(2x)+Ccos(4x)]y=0.

There are six Painlevé transcendents, corresponding to second-order ordinary differential equations whose only movable singularities are ordinary poles and which cannot be ...