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

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

The system of partial differential equations u_t = 1/2u_(xxx)+3uu_x-6ww_x (1) w_t = -w_(xxx)-3uw_x. (2)

The system of partial differential equations U_t=U·U_(xx)+U·LambdaU.

The partial differential equation 2u_(tx)+u_xu_(xx)-u_(yy)=0.

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

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) ...

The partial differential equation u_(tt)-u_(xx)-u+u^3=0.

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

A congruence of the form ax^2+bx+c=0 (mod m), (1) where a, b, and c are integers. A general quadratic congruence can be reduced to the congruence x^2=q (mod p) (2) and can be ...