How do you find all solutions of the differential equation #(d^3y)/(dx^3)=e^x#?

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Answer 1 · 2017-01-10T01:34:58

# y = e^x + Ax^2 +Bx+ C#

This is a third order separable differential equation which we can solver by repeated integration, (or separating the variables):

# (d^3y)/(dx^3)=e^x #

Integrating we get

# (d^2y)/(dx^2)=e^x + A#

And a second time:

# (dy)/(dx) = e^x + A_1x +B#

And a third time:

# y = e^x + A_1x^2/2 +Bx+ C#

So we can write the GS as;

# y = e^x + Ax^2 +Bx+ C#