Solution Found!
Is the equation t2y?(t) =(t + 4)/y2 separable?
Chapter 7, Problem 6E(choose chapter or problem)
Is the equation \(t^{2} y^{\prime}(t)=(t+4) / y^{2}\) separable?
Questions & Answers
QUESTION:
Is the equation \(t^{2} y^{\prime}(t)=(t+4) / y^{2}\) separable?
ANSWER:Problem 6E
Is the equation = separable?
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.