IDZ 11.4 - Option 14. Decisions Ryabushko AP

1. Find a particular solution of a linear homogeneous differential equation.
1.14 y + 9y = 0, y (0) = 0, y (0) = 9, y (0) = -18.

2. Solve the system of differential equations in two ways: a) information to higher order differential equations; b) using a characteristic equation.
2.14 x ´= 3x + y, y´ = x + 3y

3. Solve the differential equation by variation of arbitrary constants.
3.14 y + y = ctgx

4. Solve the following problems.
4.14 Write the equation of the curve passing through the point A (1, 2) if it is known that the product of the slope of the tangent at any point and the sum of the coordinates of the touch point is equal to twice the ordinate of this point.