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The ordinary differential equation y^('')+(1-|y|)y^'+y=0.

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

The system of ordinary differential equations X^. = sigma(Y-X) (1) Y^. = rX-Y-XZ (2) Z^. = XY-bZ. (3)

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 ordinary differential equation

If f is a continuous function that satisfies the Lipschitz condition |f(x,t)-f(y,t)|<=L|x-y| (1) in a surrounding of (x_0,t_0) in Omega subset ...

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

For a linear homogeneous ordinary differential equation, if y_1(x) and y_2(x) are solutions, then so is y_1(x)+y_2(x).

Given a nonhomogeneous ordinary differential equation, select a differential operator which will annihilate the right side, and apply it to both sides. Find the solution to ...

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.