IDZ 11.2 - Option 17. 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.

1.17 y'' = sin23x, x0 = π / 12, y (0) = -π2 / 16, y'(0) = 0.

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

2.17 2xy'y'' = y'2 + 1

• Solve the Cauchy problem for differential equations admitting a reduction of order.

3.17 y'' (1 + y) = 5y'2, y (0) = 0, y'(0) = 1.

• Integrate the following equation.

4.17 (3x2y + y3) dx + (x3 + 3xy2) 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.

5.17 A (1, -2)

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