Solve the following second order equations: (a) (b) (c) x d²y + dx² 2 dy ( 22 ) ² − ( ² ) ² = dx 2d²y dx² = 0; y(1) = 2; y'(1) = -1 +xdyy + x dx y d²y + (d) dx = In(x); y(1) = 1; y'(1) = 0 dy dx ; y(0) = 1; y'(0) = 2

Solve:y'''−5y''+33y'−29y=0y(0)=−1,  y'(0)=−18,  y''(0)=−17y(t)=

Solve y' = (y − 1)(y + 1) for y(0) = 3.

Find (6x² - 5x +4) dx. Use C for the constant. (a) What is f'(x)? (b) Find f(x), then write out the general solution.

h(x)=3(5x-2x²+6) Find h'(xr).

reduce to linear form and solve the following equation y'+(1/2x)y=x/(y^3)  y(1)=2

Calculate the first, second, and third derivatives of y(t) = 20t6/5 – 6t2". %3D (Use symbolic notation and fractions where needed.) y (1) = y"(t) = %3D y" (t) =

Based on data from 1997-2005, the amount of yogurt produced in the UnitedStates annually may be modeled byy(t) = 14.99t2 + 62.14t + 1555 million poundswhere t is the number of years since 1997.(a) Find and interpret the meaning of y(12).(b) Find and interpret the meaning of y'(12).

Let Y be the yield of an apple orchard in bushels per acre, and let x be the number of pounds of fertilizer used per acre: Y = 200 + 160x – 13x? (a) What is the yield if 3 pounds of fertilizer is used per acre? (b) What is Y'(3)? Y'(3) = bushels per pound of fertilizer