crealolobk
2021-12-16
Answered

Solve the given differential equation by undetermined coefficients

$y{}^{\u2033}+7{y}^{\prime}+6y=30$

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Stella Calderon

Answered 2021-12-17
Author has **35** answers

Consider the differential equation

$y{}^{\u2033}+7{y}^{\prime}+6y=30$ ...(1)

Rewrite the equation,$({D}^{2}+7D+6)y=30$ where $D=\frac{d}{dx}$

Auxiliary equation is,

$f\left(m\right)=0$

${m}^{3}+7m+6=0$

${m}^{2}+6m+m+6=0$

$m(m+6)+1(m+6)=0$

$(m+6)(m+1)=0$

$m=-1,-6$

Hence the complementary solution is,

$y}_{c}={c}_{1}{e}^{-x}+{c}_{2}{e}^{-6x$

Rewrite the equation,

Auxiliary equation is,

Hence the complementary solution is,

Medicim6

Answered 2021-12-18
Author has **33** answers

Can I get full answer, please. I think tha is not full.

RizerMix

Answered 2021-12-29
Author has **438** answers

Oh, sure, sorry

Apply the undetemined coefficient method to find the particular solution as follows:

Find the first and second derivatives,

Substitute these values in equation (1)

Compare the coeficients of constant and x terms,

Solve the above two equations,

Hence the particular solution is,

The general solution is,

Therefore, the required general solution is

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