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General first-order linear equations Consider the general first-order linear equation y′(t) + a(t)y(t) = f(t). This equation can be solved, in principle, by defining the integrating factor p(t) = exp(òa(t) dt). Here is how the integrating factor works. Multiply both sides of the equation by p (which is always positive) and show that the left side becomes an exact derivative. Therefore, the equation becomes
Now
48. y′(t) + 2ty(t) = 3t, y(0) = 1
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CALCULUS:EARLY TRANSCENDENTALS-PACKAGE
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