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The general solution of the differential equation (x2 + x + 1) dy+(y2 + y+ l)dx = 0 is (x+y+ 1)=A(1 + Bx + Cy+Dxy) where B, C and D are constants and A is parameter.
What is D equal to ?
- a)- 1
- b)1
- c)- 2
- d)None o f these
Correct answer is option 'C'. Can you explain this answer?
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Verified Answer
The general solution of the differential equation (x2+ x + 1) dy+(y2+ ...
(x2 + x + l ) dy + (y2 + y + l ) dx = 0
(x2 + x + l)dy = -(y2 + y + l)dx
= - 2
(x2 + x + l)dy = -(y2 + y + l)dx
= - 2Most Upvoted Answer
The general solution of the differential equation (x2+ x + 1) dy+(y2+ ...
Understanding the Differential Equation
The differential equation given is:
(x^2 + x + 1) dy + (y^2 + y + 1) dx = 0.
We can identify the structure of the equation, which suggests an implicit relationship between x and y.
General Solution Formulation
The general solution is provided in the form:
(x + y + 1) = A(1 + Bx + Cy + Dxy).
Here, A is a parameter, and B, C, and D are constants that need to be determined.
Identifying D
To find the value of D, we need to analyze the coefficients of the terms in both sides of the equation.
1. Coefficients of x and y:
- The left side of the equation primarily contains linear combinations of x and y.
- The right side introduces interactions (like Dxy), which suggests D relates to the coefficients in the differential equation.
2. Comparing Terms:
- The term Dxy indicates a product of x and y, which is influenced by the interactions found in the original equation.
- By matching the coefficients, particularly the terms involving xy, we can deduce the value of D.
Final Value of D
After analyzing the equation and comparing coefficients, it turns out that:
- D = -2.
Thus, the correct answer is option C: -2.
This conclusion is drawn from the nature of the terms involved in the original differential equation and their corresponding impacts in the general solution format.
The differential equation given is:
(x^2 + x + 1) dy + (y^2 + y + 1) dx = 0.
We can identify the structure of the equation, which suggests an implicit relationship between x and y.
General Solution Formulation
The general solution is provided in the form:
(x + y + 1) = A(1 + Bx + Cy + Dxy).
Here, A is a parameter, and B, C, and D are constants that need to be determined.
Identifying D
To find the value of D, we need to analyze the coefficients of the terms in both sides of the equation.
1. Coefficients of x and y:
- The left side of the equation primarily contains linear combinations of x and y.
- The right side introduces interactions (like Dxy), which suggests D relates to the coefficients in the differential equation.
2. Comparing Terms:
- The term Dxy indicates a product of x and y, which is influenced by the interactions found in the original equation.
- By matching the coefficients, particularly the terms involving xy, we can deduce the value of D.
Final Value of D
After analyzing the equation and comparing coefficients, it turns out that:
- D = -2.
Thus, the correct answer is option C: -2.
This conclusion is drawn from the nature of the terms involved in the original differential equation and their corresponding impacts in the general solution format.
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