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Variable separation method can be used to solve First Order, First Degree Differential Equations in which y’ is of the form.
- a)y’ = h(x)g(y)
- b)y2 = sin (h(x))
- c)y2 = cos (g(y))
- d)y3 = g(y)
Correct answer is option 'A'. Can you explain this answer?
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Variable separation method can be used to solve First Order, First Deg...
Variable separation method can be used to solveFirst Order, First Degree Differential Equations in which y’ is of the form. y’ = h(x)g(y) i.e 
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Variable separation method can be used to solve First Order, First Deg...
Understanding Variable Separation Method
The variable separation method is a powerful technique used to solve first-order, first-degree differential equations. It allows us to isolate and integrate the variables, making the solution process more straightforward.
Form of the Equation
For the method to be applicable, the differential equation must allow for the separation of variables. The correct form is:
- y = h(x)g(y)
This representation indicates that the function y can be expressed as a product of functions involving x and y. Here, h(x) is a function solely dependent on x, and g(y) is a function solely dependent on y.
Why Option A is Correct
- Separation Feasibility: In the equation y = h(x)g(y), we can rearrange it into the form where all y terms are on one side and all x terms on the other. This rearrangement is crucial for applying the variable separation technique.
- Integration: Once separated, we can integrate both sides independently with respect to their respective variables. This leads to a solution that can yield the relationship between x and y.
Other Options Explained
- Option B (y^2 = sin(h(x))): This equation does not allow for direct separation of variables as y is not expressed in a way that isolates its dependence on x and y.
- Option C (y^2 = cos(g(y))): Similarly, this form does not facilitate the separation of variables due to its structure.
- Option D (y^3 = g(y)): This representation does not have a clearly defined relationship with x, making variable separation impractical.
Conclusion
In conclusion, option A (y = h(x)g(y)) is the only form that effectively allows for the use of the variable separation method, making it the correct choice for solving first-order differential equations.
The variable separation method is a powerful technique used to solve first-order, first-degree differential equations. It allows us to isolate and integrate the variables, making the solution process more straightforward.
Form of the Equation
For the method to be applicable, the differential equation must allow for the separation of variables. The correct form is:
- y = h(x)g(y)
This representation indicates that the function y can be expressed as a product of functions involving x and y. Here, h(x) is a function solely dependent on x, and g(y) is a function solely dependent on y.
Why Option A is Correct
- Separation Feasibility: In the equation y = h(x)g(y), we can rearrange it into the form where all y terms are on one side and all x terms on the other. This rearrangement is crucial for applying the variable separation technique.
- Integration: Once separated, we can integrate both sides independently with respect to their respective variables. This leads to a solution that can yield the relationship between x and y.
Other Options Explained
- Option B (y^2 = sin(h(x))): This equation does not allow for direct separation of variables as y is not expressed in a way that isolates its dependence on x and y.
- Option C (y^2 = cos(g(y))): Similarly, this form does not facilitate the separation of variables due to its structure.
- Option D (y^3 = g(y)): This representation does not have a clearly defined relationship with x, making variable separation impractical.
Conclusion
In conclusion, option A (y = h(x)g(y)) is the only form that effectively allows for the use of the variable separation method, making it the correct choice for solving first-order differential equations.
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Variable separation method can be used to solve First Order, First Degree Differential Equations in which y’ is of the form.a)y’ = h(x)g(y)b)y2=sin(h(x))c)y2 =cos(g(y))d)y3 =g(y)Correct answer is option 'A'. Can you explain this answer? for JEE 2025 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about Variable separation method can be used to solve First Order, First Degree Differential Equations in which y’ is of the form.a)y’ = h(x)g(y)b)y2=sin(h(x))c)y2 =cos(g(y))d)y3 =g(y)Correct answer is option 'A'. Can you explain this answer? covers all topics & solutions for JEE 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Variable separation method can be used to solve First Order, First Degree Differential Equations in which y’ is of the form.a)y’ = h(x)g(y)b)y2=sin(h(x))c)y2 =cos(g(y))d)y3 =g(y)Correct answer is option 'A'. Can you explain this answer?.
Variable separation method can be used to solve First Order, First Degree Differential Equations in which y’ is of the form.a)y’ = h(x)g(y)b)y2=sin(h(x))c)y2 =cos(g(y))d)y3 =g(y)Correct answer is option 'A'. Can you explain this answer? for JEE 2025 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about Variable separation method can be used to solve First Order, First Degree Differential Equations in which y’ is of the form.a)y’ = h(x)g(y)b)y2=sin(h(x))c)y2 =cos(g(y))d)y3 =g(y)Correct answer is option 'A'. Can you explain this answer? covers all topics & solutions for JEE 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Variable separation method can be used to solve First Order, First Degree Differential Equations in which y’ is of the form.a)y’ = h(x)g(y)b)y2=sin(h(x))c)y2 =cos(g(y))d)y3 =g(y)Correct answer is option 'A'. Can you explain this answer?.
Solutions for Variable separation method can be used to solve First Order, First Degree Differential Equations in which y’ is of the form.a)y’ = h(x)g(y)b)y2=sin(h(x))c)y2 =cos(g(y))d)y3 =g(y)Correct answer is option 'A'. Can you explain this answer? in English & in Hindi are available as part of our courses for JEE.
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