IDZ 11.2 - Option 19. Decisions of Ryabushko AP

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• 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.

• Find the general solution of the differential equation that admit a lowering of the order

2.19 y''' + y''tgx = secx

• 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.

• Integrate the following equation.

4.19 (siny + ysinx + 1 / x) dx + (xcosy - cosx + 1 / y) dy = 0

• 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.

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