Evaluate the given equation for the indicated function values.
1 answer:
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a) The solution of this <em>ordinary</em> differential equation is .
b) The integrating factor for the <em>ordinary</em> differential equation is .
The <em>particular</em> solution of the <em>ordinary</em> differential equation is .
<h3>How to solve ordinary differential equations</h3>
a) In this case we need to separate each variable () in each side of the identity:
(1)
Where is the integration constant.
By table of integrals we find the solution for each integral:
If we know that and
<em>, </em>then the integration constant is
.
The solution of this <em>ordinary</em> differential equation is .
b) In this case we need to solve a first order ordinary differential equation of the following form:
(2)
Where:
- Integrating factor
- Particular function
Hence, the ordinary differential equation is equivalent to this form:
(3)
The integrating factor for the <em>ordinary</em> differential equation is .
The solution for (2) is presented below:
(4)
Where is the integration constant.
If we know that and
, then the solution of the ordinary differential equation is:
If we know that and
, then the particular solution is:
The <em>particular</em> solution of the <em>ordinary</em> differential equation is .
To learn more on ordinary differential equations, we kindly invite to check this verified question: brainly.com/question/25731911