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wolverine [178]
4 years ago
10

Solve the problem . PLEASE HELP ASAP

Mathematics
1 answer:
Natali5045456 [20]4 years ago
8 0

Answer:

\sqrt{v-1} +8=11\\\sqrt{v-1} =11-8\\v-1=(3)^{2}\\v-1=9\\v=9+1\\v=10

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If the right side of the equation dy dx = f(x, y) can be expressed as a function of the ratio y/x only, then the equation is sai
melomori [17]

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)

                         

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3 years ago
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