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The system of partial differential equations u_(xx)-u_(yy)+/-sinucosu+(cosu)/(sin^3u)(v_x^2-v_y^2)=0 (v_xcot^2u)_x=(v_ycot^2u)_y.

The ordinary differential equation (x^py^')^'+/-x^sigmay^n=0.

The Baer differential equation is given by while the Baer "wave equation" is (Moon and Spencer 1961, pp. 156-157; Zwillinger 1997, p. 121).

The partial differential equation u_t=del ·[M(u)del ((partialf)/(partialu)-Kdel ^2u)].

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

The partial differential equation u_t+del ^4u+del ^2u+1/2|del u|^2=0, where del ^2 is the Laplacian, del ^4 is the biharmonic operator, and del is the gradient.

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 partial differential equation u_t+45u^2u_x+15u_xu_(xx)+15uu_(xxx)+u_(xxxxx)=0.

The partial differential equation del ^2A=-del xE, where del ^2 is the vector Laplacian.