4. Find the solution of the vibrating string problem ᎧᎳ ᎧᎳ + əx² dy² with the boundary conditions W (0, y) = W (1, y) = 0, ᎧᎳ 1 ㅠ = cos(- 2πx) - 3 sin(5x), ду W(x,0)= = 0, 0≤x≤1, 0≤ y ≤ 1, 3π -(x,0) = cos(- +3πx). 2 Trigonometric formula cos(A + B) = cos A cos B - sin A sin B.

Q: This is the solution of the Cauchy - Euler equation xy" + 5xy' + 20y = 0 %3D O y = C1x4 cos(4 ln(x))…

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Q: 3 -2 3 2. A fundamental set of solutions of x' = 1 х is: 1

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Q: b. Determine whether the statement is true or false and justify your answer. Determine which of the…

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Q: 3. [32] −1 4-3 4. 5. [. |_3 -4 2 1 2 -1 4,

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Q: x' - x? = t, x(0) = -2, 0, 2; x(2) = 0; x(2.5) = -3, 0, 3 7. y'= sin(yx), y(0) = 0.5, 1,1.5, 2, 2.5…

A: We will use Mathematica to solve these. Each question has multiple initial value problems. 6 (a):…

Q: Find the general solution of the nonhomogeneous equation y4) + 2 y "+y=cos( 3 x) + 2 1 a) y =C,…

A: We will find out the required solution.

Q: 4 a. Consider the i.v.p x' = t^(2) + cos(x), x(0) = 0. Verify that the hypothesis of Cauchy Picard…

A: a. Verifying Conditions of Cauchy-Picard Theorem  b. Estimating the Interval of Existence

Q: dz If Z = x' sin(y), x = s²t³ and y = s°t2, %3D ds a) None of these b) 6st³ x² sin(y) – 3s²t²x³…

A: Given query is to find indicated derivative.

Q: 5) Find y' if x + cosy = Vx + sinx + xy – 1

A: Given

Q: (D-9)y 3e" +x-sin 4x. 3 1 A. y C,e*+C,e* +e* +÷x- sin 4x 25 -3x 8 3 1 B. y Ce* +C,e-* +e* -x- sin 4x…

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Q: A particular solution of y" + 2y' + 5y = e sinx 4 elsinxcosx) 13 13 2 sinx + cosx) 65 a. b. ex (355…

A: we will find the required.

Q: 1) d कर dy + 4x3 + 2y = 0,

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Q: 1. Find f(x, y) obeying = - sin(x)y and f(0, y) = }(y +2)². %3D %3D

A: Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: 1I) (3y cos(3x)dx-sin(3x)dy)/ y 0

A: Since you have asked multiple question, we will solve the first question for you. If you want any…