Find the general solution to the differential equation dydt=t3+2t2−8t Also, part 8B. asks: Show that...
David Troyer
Answered
2022-01-17
Find the general solution to the differential equation
Also, part 8B. asks: Show that the constant function is a solution.
Ive
Answer & Explanation
Maria Lopez
Expert
2022-01-18Added 32 answers
Parts of problems that say ''show that [explicitly given function] is a solution'' can be solved by simply ''plugging in''. E.g., if you're supposed to show that is a solution to the differential equation , then you should compute , compute , and ''plug them in'' to check that the differential equation is satisfied for this choice of y. You're correct that the difference in the second problem is that you no longer have the derivative with respect to t expressed as a function of t. When the equation involves both a function y and its derivative (or derivatives), it can generally be more difficult to solve. In this case, a hint I'll give you is that You can first turn things around and think of t as a function of y. You can find t(y) using similar methods to the first problem (but with a more complicated function), and then find the inverse function to get y(t).
Janet Young
Expert
2022-01-19Added 32 answers
The difference is that the main variable is y and you separate the variables to integrate and obtain the solution
Hint 1:
The first equation is very easy, so:
Hint 2:
For the other.
Then proceed integrating.
alenahelenash
Expert
2022-01-24Added 366 answers
In the first question, you are given the derivative in terms of the variable. But in the second question, you are given an expression for the derivative that involves the function. For instance, it would be one thing if you were told
(which would mean that ), and a completely different thing if you are told (this tells you that the function y is equal to its derivative; which means that for some constant A).
Actually, we can solve the second differential equation; but we dont