IDZ 11.2 - Option 27. Decisions of 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.
1.27 y´´ = 2cosxsin2x - cos3x, x0 = π / 2, y (0) = 2/3, y´(0) = 2.

2. Find the general solution of the differential equation that admit a lowering of the order
2.27 2xy´´y´ = y´2 - 4

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

4. Integrate the following equation.
4.27 (y / √ (1-x2y2) -2x) dx + xdy / √ (1-x2y2) = 0

5. Write the equation of the curve passing through the point A (x0, y0), if it is known that the intercept of the tangent to the curve on the y-axis is equal to half the sum of the coordinates of the touch.