Rewrite the following linear equation as a system of first order equation of t y' = A(t)y + g(t): y(4) ty(3) + (sint)y" - 10y = e²t.

Q: Solve the pollowing: り ( 2+J(xtjy) X=? ye! (b) (2+j)(3-j2) = a+jb a:? b:? (C) (メ-j2y) -(y-jx)-2j x=?…

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Q: The Bernoulli equation y'+37 xy'= 34 y can be converted to one of the following linear equations: a.…

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Q: P(t)y'' + Q(t)y' + R(t)y = S(t) is this a linear equation?

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Q: es of the form rar, s = x+by, wher comes u, = u. e solution of u, -uy = u with u(0, y

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Q: Please answer all and graph

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Q: Find the solution. (D-3D-2)y = 0 when x 0, y = 0 and y' 9, y" = 0 a. y = 2e- (3x-2)e* b. y 2ex+…

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Q: let h(y)=(y-3y2)5(y2+2)6  h'(y) in simplified form.

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Q: Let Y(t) = be the solution of , 6 1 Y, 5 4 -2 - Y' Y(0) 8 Write x(TT/10), round your answer to two…

A: To solve this problem first we write the system as a system of linear homogeneous differential…

Q: Solve the system Ÿ' = AŸ + Ġ for A

A: a0 A = 7-143 , B = 5505 , P = 122-1Then p-1 = 1-1 -4 -1-2-21               = 1-5 -1-2-21…

Q: y′=(3t2+4t+2)/2(y−1),y(0)=0

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Q: Solve for a linear equation? P(t)y'' + Q(t)y' + R(t)y = S(t)

A: We have to solve for a linear equationPty''+Q(t)y'+R(t)y=S(t)

Q: Rewrite the following linear equation as a system of first order equation of the form y' = A(t)y +…

A: We have to convert the given equation as a system of first order linear differential equations.…

Q: Transform the given equation into a system of first order equations (x-1)y(4) + (x+1)y'' + (tan x)y…

A: We need to transform the given equation into a system of first order equations.

Q: Solve the pollowing: () (^) 2+j =j(xtjy) X = ? y=? (1) (2+j)(3-j2) = a+jb () (x-j2y) -(y-j«)-2tj a:?…

A: (a). Given  2+j1-j = j(x+jy)⇒ 2+j1-j×1+j1+j = -y+jx⇒ 2+2j+j-11+1 = -y + jx⇒ 12+32j = -y + jxBy…

Q: Write the system y1 = -y1+2 cos(r)y3 + e 2 = xy1 - 10y2 + e" y3 +20 sin(x) Y3 = e2" y2 – a²y3 %3D…

A: The matrix form of given system of differential equations as follows

Q: Eliminate the constant: 3x 3x y=c₁e³x. + + c₂2 ve ³x схе 3 Oy" + 6y' +9y=0 Oy"-6y'+9y=0 Oy"-4y+3y=0…

A: It is given that,y=c1e3x+c2xe3xwe need to eliminate the constants c1 and c2

Q: rewrite the following second order linear equation into of two equations. y'' + 5y' - 6y = 0

A: Given y''+5y'-6y=0

Q: Find a constant solution of y′ = t2y - 5t2.

A: we have to find a constant solution of  y'=t2y-5t2

Q: If y = 2² is one solution of x²y" + 2xy' − 6y = 0, find the other linearly independent solution.

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Q: y′=2x/(1+2y),y(2)=0

A: To determine the solution of the initial value problem and determine its maximum value.

Q: -4 2 dx dt -10 4 3 with x(0) = 3 Give your solution in real form. X1 = X2 = An ellipse with…

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Q: Solve the linear equation using Gauss-Seidel -3.1x — 2.1у + 6.1z %3D 9.9 5.4х + 2.2y - 2.7z %3D 15.7…

A: Given : -3.1x-2.1y+6.1z=9.95.4x+2.2y-2.7z=15.7x+4y+3z=-24.1

Q: If y = x2 is one solution of x2y''+2xy'-6y=0 and the other linearly independent solution.

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Q: 3 ve the nonhomogeneous system tY' = (²2 =²) x + (-²₁) -21). Y (2-2)

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Q: Solve the following equations: 1. (D-D2-2D)y = 0 2. 4Dy-13Dy + 6y = 0 3. D'y - D'y – Dy + y = 0 %3D

A: On solving ist three questions we will get

Q: Find the solution. (D3 - 3D - 2)y =0; when x =0, y=0, y' = 9, y" = 0. A y = (-1+ 2x)e-2*+ e 2x B y =…

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Q: For the system, 6 -1 Y' = Y 5 4 Write the natural period of the oscillations, round the answer to…

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Q: iven are five observations for two variables, x and y. x, 12 3 4 Y, 4 7s 10 14 a) Develop a scatter…

A: Solution: x y (x-x) (x-x)2 (y-y) (x-x)(y-y) 1 4 -2 4 -4 8 2 7 -1 1 -1 1 3 5 0 0 -3 0 4…

Q: Solve the non-linear DE: ² y" + (y)² = 0

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