Answer:
y = x*sqrt(Cx - 1)
Step-by-step explanation:
Given:
dy / dx = (x^2 + 5y^2) / 2xy
Find:
Solve the given ODE by using appropriate substitution.
Solution:
- Rewrite the given ODE:
dy/dx = 0.5(x/y) + 2.5(y/x)
- use substitution y = x*v(x)
dy/dx = v + x*dv/dx
- Combine the two equations:
v + x*dv/dx = 0.5*(1/v) + 2.5*v
x*dv/dx = 0.5*(1/v) + 1.5*v
x*dv/dx = (v^2 + 1) / 2v
-Separate variables:
(2v.dv / (v^2 + 1) = dx / x
- Integrate both sides:
Ln (v^2 + 1) = Ln(x) + C
v^2 + 1 = Cx
v = sqrt(Cx - 1)
- Back substitution:
(y/x) = sqrt(Cx - 1)
y = x*sqrt(Cx - 1)
The next larger tenth is 76.1 .
The next smaller tenth is 75.9 .
Neither of those is any closer to 76 than 76 is.
76 is already rounded to the nearest tenth.
Function 2 has a greater y-intercept
<h3>Graphs</h3>
Graphs can be used to represent functions, equations, tables and relations
<h3>Equations</h3>
The equation of function 1 is given as:
To calculate the y-intercept, we set t to 0.
So, we have:
For the table of function 2, the y-intercept is 5.25
By comparison:
5.25 is greater than 5
Hence, function 2 has a greater y-intercept
Read more about graphs and functions at:
brainly.com/question/3939432
Answer:
No solution
Step-by-step explanation:
The given equations are :
9x-3y=-6
3x-y=2.....(1)
5y=15x+10
5y-15x=10
or
y-3x=2 .....(2)
Equations (1) and (2) shows that the lines are parallel. We know that for parallel lines, there is no solution.
