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john augustine
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dy/dx = xe^(y-2x) , i am asked to form differential equation using this equation . the ans given is (e^-y) = 0.5(e^-2x)(x+0.5) + a , how to get the answer? btw , i have attached my working
The equation you wrote already is a differential equation.john augustine said:dy/dx = xe^(y-2x) , i am asked to form differential equation using this equation .
Based on the answer, the problem seems to be asking you to solve the differential equation.john augustine said:the ans given is (e^-y) = 0.5(e^-2x)(x+0.5) +a
"Dy/dx" is a notation used in calculus to represent the derivative of a function y with respect to x. It represents the rate of change of y with respect to x.
To solve a differential equation such as this one, you can use techniques such as separation of variables, integrating factors, or substitution. The specific method used will depend on the form of the equation and any initial conditions given.
"e" is a mathematical constant approximately equal to 2.718. It is the base of the natural logarithm and often appears in equations involving exponential growth or decay.
Yes, this equation can be applied to real-world situations, such as modeling population growth or chemical reactions. It represents a relationship between two variables, and the solution to the equation can provide insight into the behavior of these variables.
Like any mathematical model, this equation may have limitations in its ability to accurately represent real-world situations. It may not account for all factors or variables that could affect the relationship between x and y. Additionally, the solution to the equation may have a limited range of validity.