IDZ 11.2 - Option 2. 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.
1.2 y´´´ = 1 / x, x0 = 2, y (1) = 1/4, y´(1) = y´´ (1) = 0.

2. Find the general solution of the differential equation that admit a lowering of the order
2.2 2xy´y´´ = y´2 - 1

3. Solve the Cauchy problem for differential equations admitting a reduction of order.
3.2 y´2 + 2yy´´ = k0, y (0) = 1, y´(0) = 1.

4. Integrate the following equation.
4.2 xdy-ydx / (x2 + y2) = 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 ....
5.2 A (0, 5), k = 7