IDZ 11.2 - Option 1. Decisions Ryabushko AP

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.
1.1 y´´´ = sinx, x0 = π / 2, y (0) = 1, y´(0) = 0, y´´ (0) = 0.

2. Find the general solution of the differential equation that admit a lowering of the order
2.1 (1 - x2) y´´ - xy´ = 2

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

4. Integrate the following equation.
4.1 1 / xdy-y / x2dx = 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 is equal to the ordinate of this point, an increased k times ....
5.1 A (0, 2), k = 3