1) Consider the DE x²y" – xy - 15y = 2x - 4 %3D | A) Verify that y = x and y2 = x x-3 satisfy the DE: x² y" - xy 15y 0. | B) Solve the given nonhomogeneous DE by using variation of parameters.

Q: Could y = t^2 cos t be a solution of a homogeneous DE with constant real coefficients? If so, give…

A: The solution are next step

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Q: 1 2) Find the linearization at x = a and use it to approximate f(b). f(x) = a = 6 b = 6.1 V4x+1 f(x)…

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Q: Consider the following (x²-3x+1)y" -(x²-x-2)y'+(2x-3)y=0 on the interval I = (3,00) Verify that Y₁…

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Q: Ise proper substitution to solve the following Cauchy-Euler DE [(x+1)D² – (3x+4)D+3]y = (3x + 2)e³*.…

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Q: 2. a) Find the general solution of (z²-2yz-y²)p+(xy+xz)q=xy-xz, b) which passes through the curve…

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Q: 5(a) Determine the orthogonal trajectories of the family of electric field lines described by the…

A: To find - Determine the orthogonal trajectories of the family of electric field lines described by…

Q: Find the general solution of the following: x²y" + xy' + (x² – 49)y = 0 4y" - 4y - Зу%3 0 %3D

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Q: Let z = 8x2 + 7y2, and suppose that (x, y) changes from (2, -1) to (2.01, -0.98). (a) Compute Az. Az…

A: We have to find   dz and delta z and compare the the values.

Q: Let y1, Y2 be two independent solutions of (t – 1)y" – ty' + y = 0. If W (y1, Y2)(2) = e² , then…

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Q: Give a particular solution for y" – 2y' + y = 3e*.

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Q: Are y₁ (1) = x, y₂(x) = ze² a fundamental set of solution for the equation r²y" − x(x + 2)y' + (x +…

A: Given thatand  are two solutions of DE

Q: D) (3x² – 2y + e*+Y)dx + (e**y – 2x + 4)dy = 0 (Exact) E) (2xy*e" + 2xy³ + y)dx + (x²y*e" –x²y² –…

A: Let us consider the differential equation of the form Mdx+Ndy=0 The equation is exact if ∂M∂y=∂N∂x…

Q: Suppose we are given y₁) and y2(x) (with y₁ ‡ y2), which are two different solutions of a…

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Q: Compute the solution of the IVP Sz(t) = (sin f)z(t) + sin t, l-(4) = 1, using the method for linear…

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Q: Verify by substitution that y(t) = Cekt - b/k is a solution ofy '(t) = ky + b, for real numbers b…

A: The given differential equation is y't=ky+b and the function is yt=Cekt-bk

Q: Show that Q) J3(x)=3J1(x)+4J′′ 1 (x).

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Q: = In z are two linearly indepen- of ry" + y' = 0, then the partic- - ry" + y' = f(x) can be written…

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Q: 1. Verify that y = e²x + 3xe²x is a solution of the ODE y" - 4y + 4y = 0. (Show all work when…

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Q: "+2y(y)² = 0 =1^²)={1^²/ LV=X+C₂ y(x) = c₂e¹1* - 1 . (C₂-y)² + x² = C₁ :C. -In(c 2) 71

A: Given differential equation

Q: Find the solution of z'y" + bay + (4 + 4r)y - 0, z > 0 of the form where co 1 Enter n1,2,3,...

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Q: Show that the Euler-Cauchy Equation ry" + ary + by = 0, r+0 can be transformed into the constant…

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Q: d/dt ŷ = [3 1] ŷ, ý(0) = [8] [-2 1] | [6]

A: Given that dy^dt=31-21y^ with initial condition y^(0)=86 Let A=31-21 and eigenvalue of A is λ. Then…

Q: Use the method of Frobenius to solve the given equations. a) 2x?y" – xy' + (x² + 1)y = 0 b) 2x?y" +…

A: Since the solutions of the given equations are very lengthy in Frobenius Method , i gave the…