Use the method of variation of parameters to solve the initial value problem x' = Ax + f(t), x(a) = x₂ using the following values. et 6te¹ (8t+18t²) e¹ 6te¹ 168 A = 0 1 6. f(t)= , x(0)= --- 3e¹ x(t) = 001 At 0 0

Q: Q3. Solve in terms of Bessel's function, the ODE x²y" + xy' + ((lnx)² + ¹) y = 0 1²)y=0_z=lnx.

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Q: Solve of the following Clairaut equation y=((x+4)y')+(y')^2

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Q: Solve IVP Y'=AY, A= (-3 3 Y(0) = 13 2

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Q: + ¹² = 4t, where y'(1) = 1 and y(1)=2. 4) Solve y" +

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Q: Put the equation into the form x'(t) = g(t)h(x), and solve by the method of separation of variables.…

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Q: solve by bernoulli y' + (8/x)y = x6y4

A: We will find out the required general solution for given Bernoulli's equation.

Q: Solve X'

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Q: 23. (1.4) Solve y +2 = (4x + 2y + 6)-'e2«+v+3.

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Q: Find y'

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Q: dx + 2– + x = u(1) x(0) = x'(0) = 1 dt

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Q: Find g' (6) given that f(6) = - 3 and f' (6) = 6. Enter the exact answers. (a) g(x) = 7x² – 6f (x)…

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Q: Is function  y=x2 a solution for equation of (1-x3)y'-2x+x2y+y2=0? If it is, find the solution.

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Q: Solve the initial value problem, and graph the solution function x(t). x' + 10x' +26x =…

A: Given equation contains Dirac delta function we solve by Laplace Transformation.

Q: Use the method of undetermined coefficients to determine the form of a particular solution to the…

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Q: ts1 Solve for (1+t2)y' + 4ty = f(t), y(0) = -3/4, with f (t) = { _ t 1

A: Solve

Q: Find y'. 9) y = (5x-2)(3x + 1)

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Q: Solve the IVP. (35 53 X' = X with X(0) = - (4).

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Q: Use variation of parameters to solve csc(t) y = et. sec(t).

A: Given: Let us consider the given y=12-121y+csctsectet and solve by using a variation of parameters.

Q: Calculate a) 2'/ x (-2 /½) + 2ª/s = b) Solve 2(x + 4)_ = 3(x– 2) 4 5

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