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Show that the given differential equation is homogeneous and solve them:
The given differential equation i.e., (x2 + xy) dy = (x2 + y2) dx can be written as:
This shows that equation (1) is a homogeneous equation.
To solve it, we make the substitution as:
y = vx
Differentiating both sides with respect to x, we get:
Substituting the values of v and 
in equation (1), we get:
Integrating both sides, we get:
This is the required solution of the given differential equation.
Show that the given differential equation is homogeneous and solve them:
The given differential equation is:
Thus, the given equation is a homogeneous equation.
To solve it, we make the substitution as:
y = vx
Differentiating both sides with respect to x, we get:
Substituting the values of y and 
in equation (1), we get:
Integrating both sides, we get:
This is the required solution of the given differential equation.
Show that the given differential equation is homogeneous and solve them:
The given differential equation is:
Thus, the given differential equation is a homogeneous equation.
To solve it, we make the substitution as:
y = vx
Substituting the values of y and 
in equation (1), we get:
Integrating both sides, we get:
This is the required solution of the given differential equation.
Show that the given differential equation is homogeneous and solve them:
The given differential equation is:
Therefore, the given differential equation is a homogeneous equation.
To solve it, we make the substitution as:
y = vx
Substituting the values of y and 
in equation (1), we get:
Integrating both sides, we get:
Show that the given differential equation is homogeneous and solve them:
The given differential equation is:
Therefore, the given differential equation is a homogeneous equation.
To solve it, we make the substitution as:
y = vx
Substituting the values of y and 
in equation (1), we get:
Integrating both sides, we get:
This is the required solution for the given differential equation.
Show that the given differential equation is homogeneous and solve them:
Therefore, the given differential equation is a homogeneous equation.
To solve it, we make the substitution as:
y = vx
Substituting the values of v and 
in equation (1), we get:
Integrating both sides, we get:
This is the required solution of the given differential equation.
Show that the given differential equation is homogeneous and solve them:
The given differential equation is:
Therefore, the given differential equation is a homogeneous equation.
To solve it, we make the substitution as:
y = vx
Substituting the values of y and 
in equation (1), we get:
Integrating both sides, we get:
This is the required solution of the given differential equation.
Show that the given differential equation is homogeneous and solve them:
Therefore, the given differential equation is a homogeneous equation.
To solve it, we make the substitution as:
y = vx
Substituting the values of y and 
in equation (1), we get:
Integrating both sides, we get:
This is the required solution of the given differential equation.
Show that the given differential equation is homogeneous and solve them:
Therefore, the given differential equation is a homogeneous equation.
To solve it, we make the substitution as:
y = vx
Substituting the values of y and 
in equation (1), we get:
Integrating both sides, we get:
Therefore, equation (1) becomes:
This is the required solution of the given differential equation.
Show that the given differential equation is homogeneous and solve them:
Therefore, the given differential equation is a homogeneous equation.
To solve it, we make the substitution as:
x = vy
Substituting the values of x and 
in equation (1), we get:
Integrating both sides, we get:
This is the required solution of the given differential equation.
For the given differential equation , find the particular solution satisfying the given condition:
Therefore, the given differential equation is a homogeneous equation.
To solve it, we make the substitution as:
y = vx
Substituting the values of y and 
in equation (1), we get:
Integrating both sides, we get:
Now, y = 1 at x = 1.
Substituting the value of 2k in equation (2), we get:
This is the required solution of the given differential equation.
For the given differential equation , find the particular solution satisfying the given condition:
Therefore, the given differential equation is a homogeneous equation.
To solve it, we make the substitution as:
y = vx
Substituting the values of y and 
in equation (1), we get:
Integrating both sides, we get:
Now, y = 1 at x = 1.
Substituting 
in equation (2), we get:
This is the required solution of the given differential equation.
For the given differential equation , find the particular solution satisfying the given condition:
Therefore, the given differential equation is a homogeneous equation.
To solve this differential equation, we make the substitution as:
y = vx
Substituting the values of y and 
in equation (1), we get:
Integrating both sides, we get:
Now, 
.
Substituting C = e in equation (2), we get:
This is the required solution of the given differential equation.
For the given differential equation , find the particular solution satisfying the given condition:
Therefore, the given differential equation is a homogeneous equation.
To solve it, we make the substitution as:
y = vx
Substituting the values of y and 
in equation (1), we get:
Integrating both sides, we get:
This is the required solution of the given differential equation.
Now, y = 0 at x = 1.
Substituting C = e in equation (2), we get:
This is the required solution of the given differential equation.
For the given differential equation , find the particular solution satisfying the given condition:
Therefore, the given differential equation is a homogeneous equation.
To solve it, we make the substitution as:
y = vx
Substituting the value of y and 
in equation (1), we get:
Integrating both sides, we get:
Now, y = 2 at x = 1.
Substituting C = –1 in equation (2), we get:
This is the required solution of the given differential equation.
A homogeneous differential equation of the form 
can be solved by making the substitution
For solving the homogeneous equation of the form, we need to make the substitution as x = vy.
Hence, the correct answer is C.
Which of the following is a homogeneous differential equation?
A. 
B. 
C. 
D. 
Function F(x, y) is said to be the homogenous function of degree n, if
F(λx, λy) = λn F(x, y) for any non-zero constant (λ).
Consider the equation given in alternativeD:
Hence, the differential equation given in alternative D is a homogenous equation.
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