IDZ 11.2 - Option 15. 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.
1.15 y´´´ = ex / 2 + 1, x0 = 2, y (0) = 8, y´(0) = 5, y´´ (0) = 2.

2. Find the general solution of the differential equation that admit a lowering of the order
2.15 y´´tgx = y´+ 1

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

4. Integrate the following equation.
4.15 (3x2 - 2x - y) dx + (2y - x + 3y2) 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.
5.15 A (2, 3)