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Precalculus
- Example: If ƒ (x + 2π) = ƒ (x), find the Fourier expansion f(x) = eax in the interval [−π,π]arrow_forwardPlease can you give detailed steps on how the solutions change from complex form to real form. Thanks.arrow_forwardExamples: Solve the following differential equation using Laplace transform (e) ty"-ty+y=0 with y(0) = 0, and y'(0) = 1arrow_forward
- Examples: Solve the following differential equation using Laplace transform (a) y" +2y+y=t with y(0) = 0, and y'(0) = 1arrow_forwardπ 25. If lies in the interval <0 and Sinh x = tan 0. Show that: 2 Cosh x= Sec 0, tanh x =Sin 0, Coth x = Csc 0, Csch x = Cot 0, and Sech x Cos 0.arrow_forward1 1+x 26. Derive the formula: tanhx=-In- 2 1-x ; x<1arrow_forward
- . Solve the equation for x ; tanh x = 3/5 .arrow_forwardWhat is the relationship between AdoMian decompoition method and homotopy Perturaba tion method with prove?arrow_forward21/solve the following differential equation Using laplace transform y₁ =-y, Y₁(0)=1 y' = Y Y₂(0)=0 2 21 Solve the following equations: dy 1- dt + 2y + = ydt 2 cost, y(0) = 1 2 2- y(t) = ±² + (yet) sin (t-u) du Q3: Answer the following: 1- L [Log Sa] (5²+9²) 2- L1 [Log (Cos²y1] 0-25 3-L-1 [ -] 4- (5+1) 3 L (ezt sin3t) e-s 5- L-1 ( 너 (0) 5² +5arrow_forward
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