Consider the following initial-value problem. y" - 6y = 0, y(0) = 1, y'(0) = 7 Solve the given problem first using the form of the general solution given in (10) in Section 4.3. y=c₁ekx + c₂e-kx (10) -√6x X(X) = ₁₂V6x_ + c₂e Solve again, this time using the form given in (11) in Section 4.3. y = C, cosh(kx) + C, sinh(kx) (11) Y(x) = c+cosh(v6x)+c,sinh(V6x) X

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A: The given differential equations, a) y'''-5y''+6y'+12y=0 b) y'''+3y''+y'-5y=0 c) y'v+13y''+36y=0 We…

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A: This question is about ordinary differential equation.

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A: The solution is given as

Q: Consider that Let the solution of equation y₁ = x² y2 = 3x² - y3 = 4x-2 2 x² x²y" + xy' 4y = 0…

A: All the parts are solved properly with detailed explanation.Hope you got your answer. If any query…

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Q: (a) Given Bernoulli equation xy' + 3y = 6x³, solve for appropriate solution.

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A: We have to find the particular form of the general solution.

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Q: Find the general solution of EonC(2)'y/n-1),

A: ∑i=0nnCi(2)iy(n-i)

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A: To Find:Particular solution using an undetermined coefficient.

Q: Q4. (a) Show that the substitution r= e' reduces the equation ar'y" + bry' + cy = g(x) to an…

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Q: The indicated function y₁(x) is a solution of the given differential equation. Use reduction of…

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Q: 2) Find the general solution to 2y" - y' - 6y = 0. Find the particular solution that satisfies y(0)…

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Q: if we use the method of the undetermined coefficients, the particular solution of the following D.E…

A: Here we will evaluate the required value.

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Q: Solve the initial value problem y' = 6y5 with y(0) = 3. y(x) = f(x), with f(x) = 3 To input, say,…

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Q: f' (æ) =Vx+, f(0)=2 f"(x) = 3x² 16x + 16, f'(0) = 1, ƒ(0)

A: Topic:- application of integration

Q: III Solve the differential equations (xy-6x²) dy - (2y² 9xy) dx when x = 1, y=1

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