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The partial differential equation u_(yy)=yu_(xx).

A partial function is a function that is not total.

The Helmholtz differential equation is not separable in bispherical coordinates.

The partial differential equation u_t=u_(xxx)u^3.

The partial differential equation u_t=del ·(u^mdel u).

The partial differential equation u_t=Du_(xx)+u-u^2.

In bipolar coordinates, the Helmholtz differential equation is not separable, but Laplace's equation is.

The partial differential equation u_(tt)-u_(xx)=epsilon(u_t-u_t^3).

The partial differential equation u_(xy)+(alphau_x-betau_y)/(x-y)=0.

The partial differential equation u_(xy)+alphau_x+betau_y+gammau_xu_y=0.