IDZ 11.2 - Option 20. Decisions of Ryabushko AP

1. Find a particular solution of the differential equation and calculate the value of the resulting function y = φ (x) at x = x0 to the nearest two decimal places.
1.20 y´´ = cosx + e-x, x0 = π, y (0) = -e-π, y´(0) = 1.

2. Find the general solution of the differential equation that admit a lowering of the order
2.20 y´´- 2y´ctgx = sin3x

3. Solve the Cauchy problem for differential equations admitting a reduction of order.
3.20 2y´2 = (y - 1) y´´, y (0) = 2, y´(0) = 2.

4. Integrate the following equation.
4.20 (y + sinxcos2yx) / cos2yxdx + (x / cos2yx-siny) dy = 0

5. Record equation of the curve, passing through the point A (x0, y0), and possessing a the following property: length the perpendicular dropped from the origin of coordinates onto the tangent to the curve, is equal to the abscissa the point of tangency.