Differential Equation In Exercises 43–46, find the general solution of the differential equation. Use a graphing utility to graph three solutions, one of which passes through the given point.
To calculate: The general solution of the given differential equation , and the three solutions on the graph by graphing utility.
The differential equation , and the point to find the particular solution.
The u-substitution, and
To solve the differential equation, we need to convert the equation in integral form.
So, multiply both sides of the equation by and integrate them.
The expression will look like:
So, the left-hand side of the equation will yield y, and the right side will be:
Assume , then will be:
Substitute the value of in the expression:
Substitute back the value of u in the above equation:
The above equation is the general solution of the differential equation.
To know the value of constant C of the equation,
So, the value of the constant will be .
The particular solution will be:
Similarly, take a solution for and substitute that into the general solution that has been derived
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