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 exponential property of logarithms:
Addition property of logarithmic,
To solve the differential equation, first 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:
The general equation will be:
So, the above statement can be written further as,
The above equation is the general solution of the differential equation.
To know the value of constant C of the equation, substitute the initial condition of in the general solution.
So, the value of the constant will be
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