Solve the differential equation- d2ydx2-y-0-

Given the differential equation is d^2ydx^2 y=0 .Let y=Ae^mx for A 0 be a trial solution for the given differential equation.Then we get from th ...

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Standard XII

Mathematics

Particular Solution of a Differential Equation

Solve the dif...

Question

Solve the differential equation:
$\frac{d^{2} y}{d x^{2}} - y = 0$ .

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Solution

Given the differential equation is

$\frac{d^{2} y}{d x^{2}} - y = 0$ .

Let $y = A e^{m x}$ for $A \neq 0$ be a trial solution for the given differential equation.

Then we get from the differential equation is

$m^{2} - 1 = 0$ [ Auxiliary equation]

or, $m = \pm 1$ .

So the general solution will be

$y = c_{1} e^{x} + c_{2} e^{- x}$ . [ Where $c_{1}$ and $c_{2}$ are arbitrary constants]

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Q. The solution of the differential equation

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Solve the differential equation:d2ydx2−y=0.

Given the differential equation isd2ydx2−y=0.Let y=Aemx for A≠0 be a trial solution for the given differential equation.Then we get from the differential equation ism2−1=0 [ Auxiliary equation]or, m=±1.So the general solution will be y=c1ex+c2e−x. [ Where c1 and c2 are arbitrary constants]

Solve the differential equation:
$\frac{d^{2} y}{d x^{2}} - y = 0$ .