IDZ 11.2 - Option 4. 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.
1.4 y´´´ = 6 / x3, x0 = 2, y (1) = 0, y´(1) = 5, y´´ (1) = 1.

2. Find the general solution of the differential equation that admit a lowering of the order
2.4 y´´ + y´tgx = sin2x

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

4. Integrate the following equation.
4.4 xdx + ydy + (ydx-xdy) / (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 ....
5.4 A (-2, 4), k = 6