Hint: check how you applied the rule ##\log a - \log b=\log \frac{a}{b}##.foo9008 said:Homework Statement
dy/dx = (x-y+2) / (x+y-2) , by using x=X and y=Y+2 , form a differential equation .
Homework Equations
The Attempt at a Solution
the author gave the answer as (Y^2) +(2XY) -(X^2)+A= 0 , while my answer is (Y^2) +(2XY) -(X^2)+A(X^4)= 0
is there anything wrong with my answer?
Substitution is a technique used to simplify a differential equation by replacing a variable with another expression or function.
Substitution is typically used when the original differential equation is too complex to solve directly or when the variable being substituted makes the equation easier to solve.
The steps to form a differential equation by substitution are: 1) Identify a variable to substitute, 2) Choose a new variable or expression to replace it with, 3) Substitute the new variable into the original equation, 4) Simplify and solve the resulting equation.
Yes, substitution can be used in both ordinary and partial differential equations. However, it may not always lead to a simpler equation or a solution.
One common mistake is forgetting to substitute the derivative of the new variable into the resulting equation. It is also important to check for extraneous solutions when solving the resulting equation.