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:
Step-by-step explanation:
The answer is D. Easy way to tell, the less than or equal to sign indicates a solid line in the graph. Equal=solid line. Also when you solve for y, the slope of the line (-2/3)is negative, indicating a line sloping downward.
Answer:
some circles are similar to a circle with a radius unit of 1
Step-by-step explanation:
(x-a)²
Anything to the zeroth power is equal to 1. (The numerator is equal to one because of this rule)
So.
Answer:y=-1/4x+3
Step by step explanation: i cant explain it
