IDZ 11.2 - Option 13. 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.
1.13 y´´ = arctgx, x0 = 1, y (0) = y´(0) = 0.

2. Find the general solution of the differential equation that admit a lowering of the order
2.13 xy´´ = y´ln (y´/ x)

3. Solve the Cauchy problem for differential equations admitting a reduction of order.
3.13 y´´ = 1 / y3, y (0) = 1, y´(0) = 0.

4. Integrate the following equation.
4.13 (2x + (x2 + y2) / (x2 + y)) dx = ((x2 + y2) / (xy2)) dy

5. Record equation of the curve, passing through the point A (x0, y0), if it is known, that the length of the segment, intercept on the ordinate axis normal drawn at any point of the curve, is equal to Distance from the this point of prior to the beginning of coordinates.
5.13 A (0, 1)