A) Verify that y is a solution of the ODE. B) Determine from y the particular solution of the IVP. C) Graph the solution of the IVP.1. y' + 4y = 1.4, y = ce-4x + 0.35, y(0) = 22. y' + 5xy = 0, y = ce-2.57, y(0) = 1 3. y' = y+e", y = (x + c)e", y(O) = 0.5 4. yy' = 4x, y2 - 4x² = c(y>0), y(t) = 4 5. y' = y = y2, y = 1/1 + ce-x, y(0) = 0.25 6. y'tan x = 2y—8, y = csin2 x + 4, y(pi/2) = 0

Afour cylinder four-stroke in-line engine has a stroke of 160mm, connecting rod length of 150mm, a reciprocating mass of 3kg and its firing order is 1-3-4-2. the spacing between cylinders is 100mm. i. show that the engine is in balance with regard to the primary inertia forces and primary 3. a and secondary inertia couples. li determine the out of balance secondary inertia force ii. propose ways of balancing this out of balance force and discuss the challenges that will arise

Different types of steels contain different elements that alter the characteristics of the steel. for each of the following elements, explain what the element does when alloyed with steel.

The characteristic roots of a dynamic system are: 1.7920 1.8160 i, -1.7920 1.8160 i, -0.4160 what is the order of this system? what are the settling time and damping ratio of the system?