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Find the unique solution of the second-order initial value problem.$$4 y^{\prime \prime}-4 y^{\prime}+y=0, \quad y(0)=4, y^{\prime}(0)=4$$

Calculus 3

Chapter 17

Second-Order Differential Equations

Section 1

Second-Order Linear Equations

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Find the unique solution o…

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We have 4 y plus y that old 0 y 0 is equal to y prime of 0 is equal to 4 and potan square minus 4 is 1, is equal to 2 r. Minus 1 square equal to 0 r is equal to half minute is equal to c 1 e of t divided by 2 and 2 d e f t divided by 2. Tipity 0 is just into y prime of t equal to c 1 pi by 2 times e of t divided by 2 costoomes et ivytoplus c 2 to the t divided by y prime 0, is equal to t plus c 2, which is equal to c 2. Not 02 point, so y of t is equal to 410 of the divide, 2 plus 2 times t t e e.

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