Apply Theorems 5 and 6 to find general solutions of the differential equations given in Problems 33
Question:
Apply Theorems 5 and 6 to find general solutions of the differential equations given in Problems 33 through 42. Primes denote derivatives with respect to x.
4y'' + 4y' + y = 0
Transcribed Image Text:
THEOREM 5 Distinct Real Roots If the roots ₁ and 2 of the characteristic equation in (18) are real and distinct, then y(x) = c₁e¹¹x + c₂e¹2x (19) is a general solution of Eq. (16). Thus the solution space of the equation ay" + by' + cy = 0 has basis {ex, e¹2x}.
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Related Book For
Differential Equations And Linear Algebra
ISBN: 9780134497181
4th Edition
Authors: C. Edwards, David Penney, David Calvis
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