IDZ 11.2 - Option 3. 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.
1.3 y´´ = 1 / cos2x, x0 = π / 3, y (0) = 1, y´(0) = 3/5.

2. Find the general solution of the differential equation that admit a lowering of the order
2.3 x3y´´ + x2y´ = 1

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

4. Integrate the following equation.
4.3 (2x - y + 1) dx + (2y - x - 1) 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 is equal to the ordinate of this point, an increased k times ....
5.3 A (-1, 3), k = 2