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You are watching: What are the arbitrary constants in equation 1?  In general, the number of arbitrary constants of an ordinary differential equation (ODE) is given by the bespeak of the highest possible derivative.

e.g. \$\$ycolorred"=f(x)\$\$ has \$colorred extone\$ constant of integration, \$\$ycolorred""+y"=f(x)\$\$ has \$colorred exttwo\$, \$\$ycolorred"""+y""=f(x)\$\$ has \$colorred extthree,\$ etc..

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To generalise, intend we"ve an ODE the the form \$\$a_ny^(colorgreenn)+a_n-1y^^(n-1)+cdots+a_2y""+a_1y"+a_0y=f(x), \$\$ wherein \$a_i\$ is a role of \$x\$.

Then the number of arbitrary constants in the basic solution to this equation is \$colorgreenn.\$

Notation: \$y^(n)=fracd^nydx^n\$

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answer Aug 15 "14 at 18:34 beep-boopbeep-boop
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