IDZ 11.2 - Option 18. Decisions of Ryabushko AP

IDZ 11.2 - Option 18. 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.
1.18 y´´´ = xsinx, x0 = π / 2, y (0) = 0, y´(0) = 0, y´´ (0) = 0

2. Find the general solution of the differential equation that admit a lowering of the order
2.18 y´´- y´/ (x - 1) = x (x - 1)

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

4. Integrate the following equation.
4.18 y (x2 + y2 + a2) dy + x (x2 - y2 - a2) dx = 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.

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