Step 1:

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The differential equation is $\"\"$ and the initial condition is $\"\"$ .

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Homogenous differential equation:

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If $\"\"$ is a homogenous differential equation, then to find the solution of the differential equation, we substitute $\"\"$ , where $\"\"$ is differentiable function of $\"\"$ .

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Consider $\"\"$ .

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The degree of $\"\"$ and $\"\"$ is 1.

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The differential equation is homogenous differential equation of degree 1.

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Substitute $\"\"$ and $\"\"$ in the differential equation.

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$\"\"$

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Step 2:

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$\"\"$

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Integrate on each side.

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$\"\"$

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If $\"\"$ then $\"\"$ .

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Substitute $\"\"$ in the solution of differential equation.

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Solution of the differential equation is $\"\"$ .

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The initial condition is $\"\"$ .

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

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$\"\"$

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Substitute $\"\"$ in the solution.

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$\"\"$

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Solution of the differential equation is $\"\"$ .

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Solution:

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Solution of the differential equation is $\"\"$ .