Obtain the differential equation by eliminating the arbitrary constants from the following equation: y = c₁ e2

Question 153 of 177

y = c_1 e^{2x} + c_2 e^{-2x}

Maharashtra MsbshseMaharashtra HSC (MSBSHSE) Board 2018Subjective· 2mImportance★★★★★

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Differentiate twice and eliminate $c_1, c_2$ by recognising $y''=4y$ .

Given $y = c_1e^{2x}+c_2e^{-2x}$ .

Differentiate once:

$\frac{dy}{dx} = 2c_1e^{2x}-2c_2e^{-2x}$

Differentiate again:

$\frac{d^2y}{dx^2} = 4c_1e^{2x}+4c_2e^{-2x} = 4\left(c_1e^{2x}+c_2e^{-2x}\right) = 4y$

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Q.Obtain the differential equation by eliminating the arbitrary constants from the following equation: $y = c_1 e^{2x} + c_2 e^{-2x}$ .