Solving Homogeneous Differential Equation MCQ Quiz - Objective Question with Answer for Solving Homogeneous Differential Equation - Download Free PDF

Last updated on Jun 30, 2025

Latest Solving Homogeneous Differential Equation MCQ Objective Questions

Solving Homogeneous Differential Equation Question 1:

The general solution of the differential equation  is

  1. None of the above

Answer (Detailed Solution Below)

Option 2 :

Solving Homogeneous Differential Equation Question 1 Detailed Solution

Calculation

Given equation:

Divide by x:

Let y = vx, then

Substitute in the equation:

⇒ 

⇒ 

⇒ 

Integrate both sides:

⇒ 

⇒ 

Remove the logarithms:

⇒ 

Substitute v = y/x:

⇒ 

∴ The general solution is .

Hence option 2 is correct

Solving Homogeneous Differential Equation Question 2:

The general solution of differential equation is

Answer (Detailed Solution Below)

Option 1 :

Solving Homogeneous Differential Equation Question 2 Detailed Solution

Calculation

Let

⇒ 

⇒ 

Integrating both sides:-

⇒ 

⇒ 

Hence, option 1 is correct

Solving Homogeneous Differential Equation Question 3:

The solution of the differential equation is:

Answer (Detailed Solution Below)

Option 2 :

Solving Homogeneous Differential Equation Question 3 Detailed Solution

Calculation

.....

Take,

The given equation becomes

Hence option 2 is correct

Solving Homogeneous Differential Equation Question 4:

The general solution of differential equation is

  1. None of these 

Answer (Detailed Solution Below)

Option 1 :

Solving Homogeneous Differential Equation Question 4 Detailed Solution

Calculation

Let

⇒ 

⇒ 

Integrating both sides:-

⇒ 

⇒ 

Hence, option 1 is correct

Solving Homogeneous Differential Equation Question 5:

The solution of   when  = 1 is

Answer (Detailed Solution Below)

Option 3 :

Solving Homogeneous Differential Equation Question 5 Detailed Solution

Calculation

Let , then

Integrating both sides:

Given , so

Hence option 3 is correct

Top Solving Homogeneous Differential Equation MCQ Objective Questions

Answer (Detailed Solution Below)

Option 1 :

Solving Homogeneous Differential Equation Question 6 Detailed Solution

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Concept:

Some useful formulas are:

Calculation:

Substituting y = vx and  

⇒ 

⇒ 

Integrating both sides we get,

⇒ , c = constant of integration

Putting the value of v we get,

∴ 

Answer (Detailed Solution Below)

Option 4 :

Solving Homogeneous Differential Equation Question 7 Detailed Solution

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Concept:

Some useful formulas are:

Calculation:

Substituting y=vx and 

log x = log (sinv) + log c

x = c sinv

Putting the value of v we get,

             

[Where c = constant of integration]

Answer (Detailed Solution Below)

Option 1 :

Solving Homogeneous Differential Equation Question 8 Detailed Solution

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Concept:

If a differential equation has the form f(x,y)dy = g(x,y)dx then it is said to be a homogeneous differential equation if the degree of f(x,y) and g(x, y) is the same.

Some useful formulas are;

Calculation:

Taking y = vx where  then we get

Integrating the above equation we get,

Now finally putting the value of (v = y/x) in the equation we get,

Answer (Detailed Solution Below)

Option 1 :

Solving Homogeneous Differential Equation Question 9 Detailed Solution

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Concept:

If a differential equation has the form f(x,y)dy = g(x,y)dx then it is said to be a homogeneous differential equation if the degree of f(x,y) and g(x, y) is the same.

Some useful formulas are;

Calculation:

Taking y = vx where  then we get

Integrating the above equation we get,

Now finally putting the value of y in the equation we get,

Answer (Detailed Solution Below)

Option 4 :  

Solving Homogeneous Differential Equation Question 10 Detailed Solution

Download Solution PDF

Concept:

Some useful formulas are:

Calculation:

Substituting y = vx and  

⇒ 

⇒ 

Integrating both sides we get,

⇒ , c = constant of integration

Putting the value of v we get,

∴ 

Answer (Detailed Solution Below)

Option 3 :

Solving Homogeneous Differential Equation Question 11 Detailed Solution

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Concept:

Some useful formulas are:

Calculation:

(xy + y2)dx = (x- xy)dy

Dividing both sides by xwe get,

Now substituting y = vx and 

Integrating the equation we get,

, c= constant of integration

Putting the value of v we get,

Answer (Detailed Solution Below)

Option 4 :

Solving Homogeneous Differential Equation Question 12 Detailed Solution

Download Solution PDF

Concept:

Some useful formulas are:

Calculation:

Substituting y=vx and 

log x = log (sinv) + log c

x = c sinv

Putting the value of v we get,

[Where c = constant of integration]

Solving Homogeneous Differential Equation Question 13:

If x(x + y + z) = 9, y(x + y + z) = 16, z(x + y + z) = 144, find the value of x.

  1. 169
  2. 0
  3. 13

Answer (Detailed Solution Below)

Option 3 :

Solving Homogeneous Differential Equation Question 13 Detailed Solution

Calculation:

x(x + y + z) = 9 ....(1)

y(x + y + z) = 16 ....(2)

z(x + y + z) = 144 .....(3)

By adding these three equations

x(x + y + z) + y(x + y + z) + z(x + y + z) = 9 + 16 + 144

⇒ (x + y + z)(x + y + z) = 169

⇒ (x + y + z)2 = 169

⇒ (x + y + z) = 13

From eq. (1)

⇒ x(x + y + z) = 9

⇒ x(13) = 9

⇒ x = 

Solving Homogeneous Differential Equation Question 14:

The solution of  will be

Answer (Detailed Solution Below)

Option 1 :

Solving Homogeneous Differential Equation Question 14 Detailed Solution

Concept:

Some useful formulas are:

Calculation:

Substituting y = vx and  

⇒ 

⇒ 

Integrating both sides we get,

⇒ , c = constant of integration

Putting the value of v we get,

∴ 

Solving Homogeneous Differential Equation Question 15:

The solution of the differential equation is (where C is an arbitrary constant)

Answer (Detailed Solution Below)

Option 2 :

Solving Homogeneous Differential Equation Question 15 Detailed Solution

Given:

Concept:

To solve such type of differential equations, simply put y = vx.

Calculation:

Putting y = vx

⇒  

Now, 

⇒  = v + 

⇒  = 

Integrating both sides -

⇒ ln|f(v)| = ln|x| + lnC

⇒ f(v) = Cx

putting v = y/x back,

⇒ f(y/x) = Cx

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