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posted by  VARI on 11/21/2008 8:32:05 PM  |  status: Live  

Differential EQ

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Differential Equations N/A N/A N/A
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posted by salviati on 11/21/2008 8:44:50 PM  |  status: Live
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This is a separable ODE. If we factor out the y on the left side of the equation we get separating variables and integrating we get .  After integrating we have .  Lastly we plug in our IVP data which gives us that c = 4.  So we have
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posted by roydesoto on 11/21/2008 8:47:05 PM  |  status: Live
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separate variables:



integrate both sides:



plug in initial condition:

-2 = ±√(C)

so we need the - sign in the answer, not the + sign and C = 4:
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posted by A-Rod 7821 on 11/21/2008 8:48:52 PM  |  status: Live
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"GOOD EXPLANATION I LEARN FROM IT"
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Multiply dx to both sides of the equation.

Factor out a y from the left side of the equation.
Divide (1+x2) from both sides of the equation.
Integrate both sides of the equation. On the right hand side use u-substitution. On the left hand side use the power rule of antidifferentiation:
Let u=1+x2
du=2xdx
du/(2x)=dx
The integration of
Substitute back in what you set u as: .
Initial Conditions is when y(0)= -2, x=0, y= -2.
Plug in the initial conditions: x=0, y= -2.
Plug back in the constant of integration (C)=2.
Multiply both sides of the equation by 2.
Take the square root to both sides of the equation.
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
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posted by work_able on 11/22/2008 12:57:48 AM  |  status: Live
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"NICE SOLUTION "
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