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.
1.6 y'' = 1 / (1 + x2), x0 = 1, y (0) = 0, y'(0) = 0.

2. Find the general solution of the differential equation that admit a lowering of the order
2.6 xy''- y'= x2ex

3. Solve the Cauchy problem for differential equations admitting a reduction of order.
3.6 2yy'' = y'2, y (0) = 1, y'(0) = 1.

4. Integrate the following equation.
4.6 2x (1-ey) / (1 + x2) 2dx + ey / (1 + x2) dy = 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 is equal to the ordinate of this point, an increased k times ....
5.6 A (3, -2), k = 4

Detailed solution. Designed in PDF format for easy viewing of IDZ solutions on smartphones and PCs. In MS Word (doc format) sent additionally.