prob1-5 - Problems 1-5 1. Solve: DE : y x IC: y 0 0 y 0 1 y...

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Problems 1-5 1. Solve: DE : yx   IC:  00 y   01 y   y  2. Solve: DE: 40 yy  y   y Assume that the general solution of the differential equation is 22 12 x x yc e c e  . 3. The general solution of the differential equation 2 0 xx   0 is sin cos x ct c t Find the solution satisfying the following sets of initial conditions, 0 .0 ax x x .00 bx 0 0 x v   0 cx x 0 0 x v 4. Assume is a solution of DE: y xy IC: y Without attempting to solve the equation, find   0 y and   0 y . [Itmay be assumed that exists.] 5. Consider the boundary-value problem, where f is continuous, DE: yf x   BC: y
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  10 y Show that this problem has no solution unless   f x satisfies the condition  1 0 0 fxd x which is certainly not satisfied for all functions f . Also show that when f does satisfy this condition, the solution is 00 xt y f s ds dt c  
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prob1-5 - Problems 1-5 1. Solve: DE : y x IC: y 0 0 y 0 1 y...

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