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Which one of the following is the general solution of the first order differential equation dy/dx = (x + y − 1)2, where x, y are real?
  • a)
    y = 1 + x + tan–1 (x + c), where c is a constant.
  • b)
    y = 1 + x + tan(x + c), where c is a constant.
  • c)
    y = 1 – x + tan–1 (x + c), where c is a constant.
  • d)
    y = 1 – x + tan(x + c), where c is a constant.
Correct answer is option 'D'. Can you explain this answer?
Most Upvoted Answer
Which one of the following is the general solution of the first order ...
Concept:
Variable separable: Equation of the form dy/dx = f(ax + by + c) can be reduced to variable separable form by putting ax + by + c = t
Calculation:
Given:


Substitute x + y – 1 = t

tan-1 t = x + c
t = x + y – 1
tan-1 (x + y – 1) = x + c
x + y – 1 = tan (x + c)
y = 1 – x + tan (x + c)
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Which one of the following is the general solution of the first order ...

General Solution of the First Order Differential Equation

To find the general solution of the first order differential equation dy/dx = (x + y - 1)^2, we can rewrite the equation as:

dy/(x + y - 1)^2 = dx

Integrating both sides, we get:

Integration of the Differential Equation

∫ dy/(x + y - 1)^2 = ∫ dx

Substitute u = x + y - 1

Let u = x + y - 1. Then, du = dx + dy. Substituting these into the integral, we have:

∫ du/u^2 = ∫ dx

Integrate both sides

Integrating both sides, we get:

-1/u = x + C

where C is the constant of integration.

Substitute back y = u - x + 1

Substitute u = x + y - 1 back into the equation, we get:

-1/(x + y - 1) = x + C

Solving for y, we get:

y = 1 - x + tan(x + C)

Final General Solution

Therefore, the general solution of the first order differential equation dy/dx = (x + y - 1)^2 is:

y = 1 - x + tan(x + C), where C is a constant.

So, the correct answer is option 'D'.
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Which one of the following is the general solution of the first order differential equation dy/dx = (x + y − 1)2, where x, y are real?a)y = 1 + x + tan–1(x + c), where c is a constant.b)y = 1 + x + tan(x + c), where c is a constant.c)y = 1 – x + tan–1(x + c), where c is a constant.d)y = 1 – x + tan(x + c), where c is a constant.Correct answer is option 'D'. Can you explain this answer?
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Which one of the following is the general solution of the first order differential equation dy/dx = (x + y − 1)2, where x, y are real?a)y = 1 + x + tan–1(x + c), where c is a constant.b)y = 1 + x + tan(x + c), where c is a constant.c)y = 1 – x + tan–1(x + c), where c is a constant.d)y = 1 – x + tan(x + c), where c is a constant.Correct answer is option 'D'. Can you explain this answer? for Civil Engineering (CE) 2024 is part of Civil Engineering (CE) preparation. The Question and answers have been prepared according to the Civil Engineering (CE) exam syllabus. Information about Which one of the following is the general solution of the first order differential equation dy/dx = (x + y − 1)2, where x, y are real?a)y = 1 + x + tan–1(x + c), where c is a constant.b)y = 1 + x + tan(x + c), where c is a constant.c)y = 1 – x + tan–1(x + c), where c is a constant.d)y = 1 – x + tan(x + c), where c is a constant.Correct answer is option 'D'. Can you explain this answer? covers all topics & solutions for Civil Engineering (CE) 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Which one of the following is the general solution of the first order differential equation dy/dx = (x + y − 1)2, where x, y are real?a)y = 1 + x + tan–1(x + c), where c is a constant.b)y = 1 + x + tan(x + c), where c is a constant.c)y = 1 – x + tan–1(x + c), where c is a constant.d)y = 1 – x + tan(x + c), where c is a constant.Correct answer is option 'D'. Can you explain this answer?.
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