Whats the difference between a general solution and an implicit solution of a differential equation.

Question

amistre64 · Answer

general solutions are vague and imprecise; works for a family of stuff

expplicit means that we can define one variable in terms of the others

implicit means the equation cant really be broken down into something useable

amistre64 · Answer

y^2 - y = sin(x)

solve for y  is difficult so we say its implicit; or implied that y is a function of x

amistre64 · Answer

y = tan(x)-3x  is explicitly stating y as a function of x

amistre64 · Answer

.... of course it helps of i can read ...

anonymous · Answer

so after you have simplified as much as you can and cant go any further leave the equation as an implicit answer

amistre64 · Answer

ok, a general solution is one of a family; involves arbitrary constants

amistre64 · Answer

correct