y^4=5y^1+5y^1 25y ⇒ y^4 10y^1+25y=0 A.E #160; m^2 10m+25=0 m=5, 5 ∴ y=(c_1x+c_2)e^5x ...

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Particular Solution of a Differential Equation

Solve y”=5y...

Question

Solve $y^{''} = 5 y^{'} + 5 (y^{'} - 5 y)$ .

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Solution

$y^{4} = 5 y^{1} + 5 y^{1} - 25 y$
$\Rightarrow y^{4} - 10 y^{1} + 25 y = 0$
A.E $m^{2} - 10 m + 25 = 0$
$m = 5, 5$
$∴ y = (c_{1} x + c_{2}) e^{5 x}$

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