IDZ 11.2 - Option 8. 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.

1.8 y''' = e2x, x0 = 1/2, y (0) = 9/8, y'(0) = 1/4, y'' (0) = -1/2.

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

2.8 x2y'' + xy' = 1

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

3.8 y'' = -1 / (2y3), y (0) = 1/2, y'(0) = √2.

• Integrate the following equation.

4.8 (1 - ex / y) dx + ex / y (1 - x / y) 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.

5.8 A (3, -1), n = 3/2

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