$\"\"$

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The homogeneous differential equation is $\"\"$ .

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The standard form of homogeneous differential equation is $\"\"$ .

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If the differential equation is homogeneous, then substitute $\"\"$ .

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$\"\"$

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Apply derivative on each side with respect to $\"\"$ .

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$\"\"$

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Apply product rule of differentiation: $\"\"$ .

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$\"\"$ .

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$\"\"$ .

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$\"\"$

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Substitute $\"\"$ and $\"\"$ in $\"\"$ .

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$\"\"$

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$\"\"$

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$\"\"$

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$\"\"$

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$\"\"$

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$\"\"$

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$\"\"$

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$\"\"$

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Apply integral on each side.

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$\"\"$

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$\"\"$

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$\"\"$

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Apply formula: $\"\"$ .

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$\"\"$

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$\"\"$

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$\"\"$

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$\"\"$

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Substitute $\"\"$ .

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$\"\"$

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$\"\"$

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Exponentiate each side.

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$\"\"$

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$\"\"$

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$\"\"$

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$\"\"$ .

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The solution of differential equation is $\"\"$ .

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$\"\"$

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$\"\"$ .