Solve the equation?

Question

Solve the equation y"'(t)-2=0 by computing successive antiderivatives.

Answer 1

Start by getting 2 on the other side. 

y'''(t) = 2,  take the integral of both sides and you get,

y''(t) = 2t + a. "a" is just a constant. Do the next integral,

y'(t) = t^2 + a*t + b. Take the final integral

y(t) = 1/3*t^3 + a/2*t^2 + b*t + c. You can simple a/2 to just a since "a" just represents an unknown constant. For a final equation:

y(t) = 1/3*t^3 + a*t^2 + b*t + c

 

Answer 2

this can be written as y'''(t) = 2   

integrate both sides to get y''(t) = 2t + c where c is any constant

integrate both sides again to get y'(t) = t^2 + cx + c where each c is any constant

integrate both sides again to get y(t) = (1/3)x^3 + (c/2)x^2 + cx + c where all c are any constants