 # IDZ 11.2 - Option 19. Decisions of Ryabushko AP

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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.
1.19 y´´´sin4x = sin2x, x0 = 5π / 2, y (π / 2) = π / 2, y´(π / 2) = 1, y´´ (π / 2) = -1.

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

3. Solve the Cauchy problem for differential equations admitting a reduction of order.
3.19 4y´´2 = 1 + y´2, y (0) = 1, y´(0) = 0.

4. Integrate the following equation.
4.19 (siny + ysinx + 1 / x) dx + (xcosy - cosx + 1 / y) 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. 