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.
1.7 xy´´´ = 2, x0 = 2, y (1) = 1/2, y´(1) = y´´ (1) = 0.

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

3. Solve the Cauchy problem for differential equations admitting a reduction of order.
3.7 yy´´- y´2 = y4, y (0) = 1, y´(0) = 1.

4. Integrate the following equation.
4.7 2x / y3dx + y2-3x2 / y4dy = 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 in n is greater than the slope of the straight line connecting the same point with the origin.
5.7 A (2, 5), n = 8