How do you integrate this differential equation then solve it? - Equation included

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Assumption x=0 when v=0

1 Answer
Jun 8, 2018

Given: vdvdx=9.80.004v2,v(0)=0

Use the separation of variables method:

v9.80.004v2dv=dx

Integrate both sides:

v9.80.004v2dv=dx

Multiply by 1 in the form of 250250:

(250250)v9.80.004v2dv=dx

1252vv22450dv=dx

Let u=v2 then du=2dv:

1251u2450du=dx

ln(u2450)=x125+C

Reverse the substitution:

ln(v22450)=x125+C

v22450=e0.008x+C

v2=2450+Ce0.008x

Use the boundary condition:

02=2450+C

C=2450

v2=24502450e0.008x

v2=2450(1e0.008x) Q.E.D.