Solution Found!
Explain how to solve a separable differential equation of
Chapter 7, Problem 7E(choose chapter or problem)
Explain how to solve a separable differential equation of the form \(g(y) y^{\prime}(t)=h(t)\).
Questions & Answers
QUESTION:
Explain how to solve a separable differential equation of the form \(g(y) y^{\prime}(t)=h(t)\).
ANSWER:Problem 7E
Explain how to solve a separable differential equation of the form g(y) y′(t)= h(t).
Answer;
Step 1;
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;
- 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.