IDZ 11.2 - Option 10. 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.
1.10 y´´ = 1 / √ (1 - x2), x0 = 1, y (0) = 2, y´(0) = 3.

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

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

4. Integrate the following equation.
4.10 (3x2 + 6xy2) dx + (6x2y + 4y3) dy = 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.
5.10 A (-8, -2), n = 3