Solved: 4548. General first-order linear equations

Chapter , Problem 48

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4548. General first-order linear equations Consider the general first-order linear equation y1t2 + a1t2y1t2 = f 1t2. This equation can be solved, in principle, by defining the integrating factor p1t2 = exp1 1a1t2 dt2. 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 p1t21y1t2 + a1t2y1t22 = d dt 1p1t2y1t22 = p1t2 f 1t2. Now integrate both sides of the equation with respect to t to obtain the solution. Use this method to solve the following initial value problems. Begin by computing the required integrating factor. y_1t2 + 2ty1t2 = 3t, y102 = 1

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