IDZ 11.2 - Option 9. 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.

1.9 y''' = cos2x, x0 = π, y (0) = 1, y'(0) = -1/8, y'' (0) = 0.

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

2.9 y'' = -x / y'

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

3.9 y'' = 1 - y'2, y (0) = 0, y'(0) = 0.

• Integrate the following equation.

4.9 x (2x2 + y2) + y (x2 + 2y2) y '= 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.

5.9 A (-6, 4), n = 9

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