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The solution of the differential equation dy/dx = y/x with y(1) = 1 is
- a)y=x
- b)y=x2
- c)log(x) + log(y) = 0
- d)log(x) - log(y) = 1
Correct answer is option 'A'. Can you explain this answer?
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The solution of the differential equation dy/dx = y/x with y(1) = 1 is...
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The solution of the differential equation dy/dx = y/x with y(1) = 1 is...
Dy/dx =y/x
by variable separable
dy/y=dx/x
logy=log+logc
logy=logxc
y=xc
given condition y(1)=1 ,we get c=1
required equation
y=x
by variable separable
dy/y=dx/x
logy=log+logc
logy=logxc
y=xc
given condition y(1)=1 ,we get c=1
required equation
y=x
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The solution of the differential equation dy/dx = y/x with y(1) = 1 is...
Given:
The differential equation is dy/dx = y/x with y(1) = 1.
To find:
The solution to the differential equation.
Solution:
To solve the differential equation, we can use the method of separation of variables.
Step 1: Separate the variables by multiplying both sides of the equation by x and dividing both sides by y:
x dy = y dx.
Step 2: Integrate both sides of the equation:
∫x dy = ∫y dx.
Step 3: Evaluate the integrals:
x^2/2 + C1 = y^2/2 + C2.
Step 4: Combine the constants of integration:
x^2/2 + C1 = y^2/2 + C2.
Step 5: Rewrite the equation in terms of y:
y^2 = x^2 + C.
Step 6: Apply the initial condition y(1) = 1 to find the value of the constant C:
1^2 = 1^2 + C
1 = 1 + C
C = 0.
Step 7: Substitute the value of C back into the equation:
y^2 = x^2 + 0
y^2 = x^2.
Step 8: Take the square root of both sides:
y = ±x.
Note: Since the initial condition y(1) = 1 is given, we can determine that the solution to the differential equation is y = x (option A). The negative square root solution does not satisfy the initial condition.
The differential equation is dy/dx = y/x with y(1) = 1.
To find:
The solution to the differential equation.
Solution:
To solve the differential equation, we can use the method of separation of variables.
Step 1: Separate the variables by multiplying both sides of the equation by x and dividing both sides by y:
x dy = y dx.
Step 2: Integrate both sides of the equation:
∫x dy = ∫y dx.
Step 3: Evaluate the integrals:
x^2/2 + C1 = y^2/2 + C2.
Step 4: Combine the constants of integration:
x^2/2 + C1 = y^2/2 + C2.
Step 5: Rewrite the equation in terms of y:
y^2 = x^2 + C.
Step 6: Apply the initial condition y(1) = 1 to find the value of the constant C:
1^2 = 1^2 + C
1 = 1 + C
C = 0.
Step 7: Substitute the value of C back into the equation:
y^2 = x^2 + 0
y^2 = x^2.
Step 8: Take the square root of both sides:
y = ±x.
Note: Since the initial condition y(1) = 1 is given, we can determine that the solution to the differential equation is y = x (option A). The negative square root solution does not satisfy the initial condition.
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Question Description
The solution of the differential equation dy/dx = y/x with y(1) = 1 isa)y=xb)y=x2c)log(x) + log(y) = 0d)log(x) -log(y) = 1Correct answer is option 'A'. Can you explain this answer? for IIT JAM 2025 is part of IIT JAM preparation. The Question and answers have been prepared according to the IIT JAM exam syllabus. Information about The solution of the differential equation dy/dx = y/x with y(1) = 1 isa)y=xb)y=x2c)log(x) + log(y) = 0d)log(x) -log(y) = 1Correct answer is option 'A'. Can you explain this answer? covers all topics & solutions for IIT JAM 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The solution of the differential equation dy/dx = y/x with y(1) = 1 isa)y=xb)y=x2c)log(x) + log(y) = 0d)log(x) -log(y) = 1Correct answer is option 'A'. Can you explain this answer?.
The solution of the differential equation dy/dx = y/x with y(1) = 1 isa)y=xb)y=x2c)log(x) + log(y) = 0d)log(x) -log(y) = 1Correct answer is option 'A'. Can you explain this answer? for IIT JAM 2025 is part of IIT JAM preparation. The Question and answers have been prepared according to the IIT JAM exam syllabus. Information about The solution of the differential equation dy/dx = y/x with y(1) = 1 isa)y=xb)y=x2c)log(x) + log(y) = 0d)log(x) -log(y) = 1Correct answer is option 'A'. Can you explain this answer? covers all topics & solutions for IIT JAM 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The solution of the differential equation dy/dx = y/x with y(1) = 1 isa)y=xb)y=x2c)log(x) + log(y) = 0d)log(x) -log(y) = 1Correct answer is option 'A'. Can you explain this answer?.
Solutions for The solution of the differential equation dy/dx = y/x with y(1) = 1 isa)y=xb)y=x2c)log(x) + log(y) = 0d)log(x) -log(y) = 1Correct answer is option 'A'. Can you explain this answer? in English & in Hindi are available as part of our courses for IIT JAM.
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