IDZ 11.2 - Option 5. 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.
1.5 y´´ = 4cos2x, x0 = π / 4, y (0) = 1, y´(0) = 3.

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

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

4. Integrate the following equation.
4.5 (x / √x2-y2-1) dx-ydy / √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 ....
5.5 A (-2, 1), k = 5