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.
1.16 y'' = x / e2x, x0 = -1/2, y (0) = 1/4, y'(0) = -1/4.

2. Find the general solution of the differential equation that admit a lowering of the order
2.16 y'' + 2xy'2 = 0

3. Solve the Cauchy problem for differential equations admitting a reduction of order.
3.16 y'' + 2 / (1-y) y'2 = 0, y (0) = 0, y'(0) = 1.

4. Integrate the following equation.
4.16 (xdx + ydy) / √ (x2 + y2) + (xdy-ydx) / x2 = 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.
5.16 A (-4, 1)

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