is the following equation homogenous equation: dy/dx =(x^2-y^2)/xy Solution i) T
ID: 1892809 • Letter: I
Question
is the following equation homogenous equation: dy/dx =(x^2-y^2)/xyExplanation / Answer
i) Taking in proper brackets, your question suppose to be: dy/dx = (x² + 3y²)/2xy ii) Let y = vx and differentiating, dy/dx = v + x*(dv/dx) iii) ==> v + x*(dv/dx) = (1 + 3v²)/2v This simplifies as: (2v)dv/(1 + v²) = dx/x Integrating, ln|1 + v²| = ln|x| + C Substituting v = y/x and simplifying, Ans: (x² - y²) = C*(x³) EDIT: @Rapidfir: Can't you read the solution before marking TD? It is atrocious! Clearly in first line I stated "Taking in proper brackets, your question suppose to be: dy/dx = (x² + 3y²)/2xy" and provided the solution accordingly. It is up to the questioner to decide whether it is correct or wrong. Invariably about 95% of the questioners are unaware of presenting the questions with proper brackets. Only those who are answering may have to reasonably read the question, understand and provide the solution. Further this question is quite common in this topic and definitely it is not presented with proper brackets. Further, for your kind information, I am in teaching line for more than 4 decades and very much aware of 'BODMAS' rule. My approach in teaching is: 'Don't discourage anyone for wrong doing; but try to correct them with proper guidance'.
Related Questions
Navigate
Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.