wolfsaway
29.06.2019 •
Mathematics
Consider the differential equation x^2 y''-xy'-3y=0. if y1=x3 is one solution use redution of order formula to find a second linearly independent solution
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Ответ:
Suppose is another solution. Then
Substituting these derivatives into the ODE gives
Let , so that
Then the ODE becomes
and we can condense the left hand side as a derivative of a product,
Integrate both sides with respect to :
Solve for :
Solve for :
So another linearly independent solution is .
Ответ:
point
step-by-step explanation:
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