Slove the first - order differential equation by any appropriate method.

Question

Slove the <!--td {border: 1px solid #ccc;}br {mso-data-placement:same-cell;}--> first - order differential equation by any appropriate method.

Answer 1

Step 1:

The first order differential equation is .

The standard form of linear differentiation equation is  .

Solve the differential equation by converting into linear differentiation equation.

Divide each side by .

Step 2:

Consider .

Apply derivative on each side with respect to .

Substitute and in .

The above equation is in the form of linear differentiation equation .

Compare with .

Where and .

In linear differentiation, substitute .

.

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Step 3:

The solution of linear differentiation equation is .

Substitute and .

Back substitute in .

.

Solution:

The solution is .