IDZ 11.2 - Option 17. 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.
1.17 y´´ = sin23x, x0 = π / 12, y (0) = -π2 / 16, y´(0) = 0.

2. Find the general solution of the differential equation that admit a lowering of the order
2.17 2xy´y´´ = y´2 + 1

3. Solve the Cauchy problem for differential equations admitting a reduction of order.
3.17 y´´ (1 + y) = 5y´2, y (0) = 0, y´(0) = 1.

4. Integrate the following equation.
4.17 (3x2y + y3) dx + (x3 + 3xy2) dy = 0

5. Record equation of the curve, passing through the point A (x0, y0), and possessing a the following property: length the perpendicular dropped from the origin of coordinates onto the tangent to the curve, is equal to the abscissa the point of tangency.
5.17 A (1, -2)