Solve : Find Exactly

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  • #1
karush
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\tiny{b.2.1.23}
1000
Solve the initial value problem and find the critical value exactly.

divide by 3

with integrating factor multiply through

ok just seeing if this is going in the right direction
 
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  • #2
It's easy to check. If is an integrating factor then so, yes, that is the correct integrating factor.To complete, integrate both sides of which is, of course, the same as including the constant of integration, using the condition that y(0)= 1 to determine the value of that constant.

Since this is a "linear equation with constant coefficients" it can also be done, perhaps more easily, by solving the "characteristic equation", so meaning that the general solution to the "associated homogeneous equation", 3y'- 2y= 0, is where C is an undetermined constant. We then look for a single function to satisfy the entire equation . Since the right side is a contant, we try y= A so that y'= 0 and the equation becomes so that and the general solution to the entire equation is . Use to determine the value of C.
 
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