Solve the given third-order differential equation by variation of parameters. y''' − 5y'' − y' + 5y = e4x
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Answer:
Step-by-step explanation:
When we multiply a polynomial by a specific monomial, all terms in the polynomial get multiplied by the monomial.
So we can do this by term.
Multiplying x by x to the something power will just increase the exponent on the x term by one (since powers are just x multiplied by itself). This means the exponent here will increase by 1, so this becomes .
Same logic applies to the second term: , raise the exponent by one,
.
For the third term, if there is no exponent on a term you can assume it's exponent is 1 (so in this case - as
). Again, using the same logic, this turns into
.
For the last term, when we multiply a constant by a variable, we get a term with a variable and a coefficient - the constant becomes the coefficient and the variable stays the variable. Therefore, .
Adding these terms all together gets us .
Hope this helped!
