 # IDZ 11.2 - Option 9. Decisions Ryabushko AP

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1. 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.

2. Find the general solution of the differential equation that admit a lowering of the order
2.9 y´´ = -x / y´

3. Solve the Cauchy problem for differential equations admitting a reduction of order.
3.9 y´´ = 1 - y´2, y (0) = 0, y´(0) = 0.

4. Integrate the following equation.
4.9 x (2x2 + y2) + y (x2 + 2y2) y ´= 0

5. 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 