Solved: 3336. Special equations A special class of

Chapter , Problem 33

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3336. Special equations A special class of first-order linear equations have the form a1t2y1t2 + a1t2y1t2 = f 1t2, where a and f are given functions of t. Notice that the left side of this equation can be written as the derivative of a product, so the equation has the form a1t2y1t2 + a1t2y1t2 = d dt 1a1t2y1t22 = f 1t2. Therefore, the equation can be solved by integrating both sides with respect to t. Use this idea to solve the following initial value problems. ty_1t2 + y = 1 + t, y112 = 4

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