IDZ 11.2 - Option 28. 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.
1.28 y´´ = x - lnx, x0 = 2, y (1) = -5/12, y´(1) = 3/2.

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

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

4. Integrate the following equation.
4.28 (5x4y4 + 28x6) dx + (4x5y3 - 3y2) dy = 0

5. Write the equation of the curve passing through the point A (x0, y0), if it is known that the intercept of the tangent to the curve on the y-axis is equal to half the sum of the coordinates of the touch.