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Separable differential equations Find the general solution
Chapter 7, Problem 24E(choose chapter or problem)
Separable differential equations Find the general solution of the following equations.
\(\frac{d y}{d x}=y\left(x^{2}+1\right)\), where y>0
Questions & Answers
QUESTION:
Separable differential equations Find the general solution of the following equations.
\(\frac{d y}{d x}=y\left(x^{2}+1\right)\), where y>0
ANSWER:Step 1 of 3
DEFINITION : A differential equation is said to be of type “variable separable” if it can be expressed in such a way , so that the coefficient of dx is a function of of x alone and the coefficient of dy is a function of y alone.
The general form of such differential equation can be written as
f(x) dx = g(y)dy ……………….(1)
Integrating both sides and adding an arbitrary constant C , we get the general solution as
f(x)dx =
+C
Working rule of solving by the method of separation of variables;
1. Write the given differential equation in the form
f(x) dx = g(y)dy
That is make the coefficient of dx as an expression of x alone and that of dy as an expression of y alone
2. Integrate both sides and add an arbitrary constant to any one side and get the general solution.