hadejada7x
2021-12-27
Answered

Find the general solutions of the differential equations $6{y}^{4}+11y4y=0$

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Mary Nicholson

Answered 2021-12-28
Author has **38** answers

Eq (1) can be written as

AE.

For value of m we put

Which is comple roots.

Mary Nicholson

Answered 2021-12-29
Author has **38** answers

The auxilary equation is,

$6{m}^{4}+11{m}^{2}+4=0$

$\Rightarrow {m}^{2}=\frac{-11\pm \sqrt{121-96}}{12}=\frac{-1}{2},\frac{-4}{3}$

$\Rightarrow m=\pm \frac{i}{\sqrt{2}},\pm \frac{2i}{\sqrt{3}}$

If$\alpha \pm i\beta$ are the roots of auxilary equation, then the solution is $y={e}^{\alpha x}({c}_{1}\mathrm{cos}\beta x+{c}_{2}\mathrm{sin}\beta x)$

Thus, the required solution is,

$y=({c}_{1}\mathrm{cos}\frac{x}{\sqrt{2}}+{c}_{2}\mathrm{sin}\frac{x}{\sqrt{2}})+({c}_{3}\mathrm{cos}\frac{2x}{\sqrt{3}}+{c}_{4}\mathrm{sin}\frac{2x}{\sqrt{3}})$

If

Thus, the required solution is,

karton

Answered 2022-01-10
Author has **439** answers

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Ostensibly, it seems that

At least that's the form that I think I've been taught. Problem is that it just doesn't work out for me. I get a value for A, but not for B... Am I choosing an incorrect yp form?