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Step 1 :

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The differential equation is $\"\"$

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Consider $\"\"$ .

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The auxiliary equation is $\"\"$ .

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Find the roots of the auxiliary equation.

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$\"\"$

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The roots of the auxiliary equation $\"\"$ .

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The complementary solution is $\"\"$

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Step 2 :

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Find the particular solution.

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The particular solution is of the form $\"\"$ .

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Apply derivative on each side with respect to x.

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$\"\"$

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Apply derivative on each side with respect to x.

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$\"\"$

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Substitute $\"\"$ and $\"\"$ in equation (1).

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$\"\"$

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The particular solution is $\"\"$ .

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The general solution is $\"\"$ .

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Solution :

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The general solution is $\"\"$ .

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