IDZ 11.2 - Option 23. 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.
1.23 y´´ = 1 / cos2 (x / 2), x0 = 4π, y (0) = 0, y´(0) = 1.

2. Find the general solution of the differential equation that admit a lowering of the order
2.23 x (y´´ + 1) + y´= 0

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

4. Integrate the following equation.
4.23 (y / 2√ (xy) + 2xysinx2y + 4) dx + (x / 2√ (xy) + x2sinx2y) dy = 0

5. Write the equation of the curve passing through the point A (x0, y0), and has the property segment, which is the tangent at any point on the curve cuts the axis Oy, is equal to the square of the abscissa of the point of contact.