IDZ 11.2 - Option 10. Decisions 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.

1.10 y'' = 1 / √ (1 - x2), x0 = 1, y (0) = 2, y'(0) = 3.

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

2.10 xy'' = y'

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

3.10 y''2 = y', y (0) = 2/3, y'(0) = 1.

• Integrate the following equation.

4.10 (3x2 + 6xy2) dx + (6x2y + 4y3) dy = 0

• Write the equation of the curve passing through the point A (x0, y0), if it is known that the slope of the tangent at any point in n is greater than the slope of the straight line connecting the same point with the origin.

5.10 A (-8, -2), n = 3

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