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The partial differential equation u_t+2uu_x-nuu_(xx)+muu_(xxx)=0.

The second-order ordinary differential equation y^('')+alpha(x)y^'+x^2y^n=0.

An indicial equation, also called a characteristic equation, is a recurrence equation obtained during application of the Frobenius method of solving a second-order ordinary ...

The most general forced form of the Duffing equation is x^..+deltax^.+(betax^3+/-omega_0^2x)=gammacos(omegat+phi). (1) Depending on the parameters chosen, the equation can ...

The second-order ordinary differential equation xy^('')+(c-x)y^'-ay=0, sometimes also called Kummer's differential equation (Slater 1960, p. 2; Zwillinger 1997, p. 124). It ...

The third-order ordinary differential equation y^(''')+alphayy^('')+beta(1-y^('2))=0.

A Fredholm integral equation of the second kind phi(x)=f(x)+lambdaint_a^bK(x,t)phi(t)dt (1) may be solved as follows. Take phi_0(x) = f(x) (2) phi_1(x) = ...

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

The partial differential equation u_t+u_x-6uu_x-u_(txx)=0.

A Fredholm integral equation of the first kind is an integral equation of the form f(x)=int_a^bK(x,t)phi(t)dt, (1) where K(x,t) is the kernel and phi(t) is an unknown ...