Answer:
Step-by-step explanation:
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)
Answer:
answer is J because if we lay out the information we will understand it
Okay first you need to combine like terms together (3x and 1x)
7x + 4 = 5 + 4x
now you need x only on one side, you could subtract either 7x or 4x
3x + 4 = 5
subtract 4 over
3x = 1 is the answer
Solution :
Given, the equation .
To graph the equation on the coordinate plane, we first need to derive the different points of the equation ,
The graph plotted using these points is shown in the figure,