Find the general solution of y""- 6y"+21y'- 26y=0 3x A y=c,e"+c,e cos 2x +c,e"sin 2x 2x В y=c,e"+c,e* cos 3x+c,e"sin 3x © y=c,e -2x 2xsin 3x cos 3x +c y=c,e-2"+c, 3x cos 2x+C ,e" 3x sin 2x

Q: The dynamics of the variable ywith respect to variable xis described by the following stiff ODE: dy…

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Q: Solve the initial value problem. * = et sin (et - 4), y(ln 4) = 0 %3D O A) y = -cos (et - 4) + 1 %3D…

A: Given:-   D.E:dydt=et sm et -4                  Initial condition: y ln 4=0   To calculate:…

Q: Evaluate (x²sin y-xcos(y)) dy A x²(1+ sin(1))-xcos (1) + C B x²(1-cos(1))-xsin (1) + C C 2sin…

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Q: Consider the following IVP: y" +y' = -cos x; y(0) = a, y'(0) = b Find the general solution. A y(x) =…

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Q: 1. Find the general solution of y'= cos²xcosy

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Q: If y = 12y sin(4z) – 12z sin(4y), then (z, y) = 6y? sin(4z) + 3z cos(4y) + h(x) O (z, y) = 6y²…

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Q: - (Ax + B) - Ar + B where A = acz and B = bez. When i--a 0, the differential equation becomes X* +…

A: By using relationship between trigonometric, hyperbolic and exponential functions you can solve the…

Q: Find the general solution of y(4)+y'' = 3t2+4sin t-2 co

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Q: Give the form of a particular solution of -4x yl4) – 256 y =2 e**+3 e+ cos(4 x) – 2 a) O z=Ae -4х +…

A: OPTION D IS CORRECT.

Q: Obtain general solution   y¹ = cos²x cos y

A: Obtain general solution  y¹ = cos²x cos y

Q: 2. Show that u(x, t) = cos(x – ct) is a solution of Ut + cuz = (0

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Q: x³y"+xy'+4y = cos (2 In x)

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Q: Find the general solution of y'=cos²xcosy

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Q: dl ) Verify that y = C₁ cos(3x) + c₂sin(3x) is a solution of 2); A) (::. - y" +9y = 0 B) {….. y' +…

A: Solution

Q: y′= (6xe^(6x)) X (cos^(2) (6y)) a) Write the equation in an integrable form by separating it into…

A: Solve using variable separable method.

Q: Use the annihilator operator (not undetermined coefficient) for the right hand side and use it with…

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Q: Differentiate y=excos(x2): y'= A. excos(x2)-2xsin(x2) B. -2xexsin(x2) C. ex(cos(x2)-2xsin(x2))…

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Q: 5. Obtain the particular solution. y'"-2 y'+2 y=3e" cos 2x; when x 0, y=2,y'=3

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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: 1. y" - 2y' - 3y = 5e¹, y(0) = 1, y'(0) = 0 2. y" + 2y + 5y = 3 sin(2x) 3. y" - 4y + 4y = -7x+4x²,…

A: Since you have posted multiple questions. As per guidelines we"ll solve only  first question. If you…

Q: Find the General Solution: (show solution) 1.(x3+xy2-y)dx –(x-x2y-y3)dy=0   Ans: (x2+y2)2-4xy+C=0

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Q: 3. Rewrite y" - 2y' + y² = cos x as two first-order equations and then use Euler's method to…

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Q: 2. Differentiate y os=1(-2x³ – 3)³ = cOs

A: From the given problem:   y=cos-1-2x3-33   As we know that:   cos-1x=-11-x2   So,…

Q: Integrate with respect to x: sin(3x) a b 2 cos(4x) cos (2r) (5) f e2x cos² () d 3 cos 3 sin(2a) — е…

A: We have to solve the following integral .

Q: 2. If y = C₁ cos2x+C₂ sin 2x+2sin x is the general solution of a certain nonhomogeneous LDE, which…

A: The given general solution of non-homogeenous  LDE.  y= c1cos2x +c2sin2x +2sinx   We have to find…

Q: 9. Use the method of undetermined coefficients to solve the given system sin t X' X + %3D -2 cos

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Q: The general solution of y" + 16y3 cost is: Select one: a. y= C, cos(4t) + C2 sin(4t) + 1 -tcost 15 O…

A: Using Solution of Linear Differential Equation

Q: - Second order : non- homogeneous Equations with Constant Coefficients d²y 4-- + 16y = 10 cos 4x dx²

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Q: 2 Find the general Solution of yty = 2xcosx -CosX %3D

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Q: Show that y1(t) = cos(3t) and y2(t) = sin(3t) are linearly independent for all t

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Q: Verify that y = 7 sin 2x + 9 cos 2x is a solution of y" + 4y = 0 %3D

A: Given, y = 7sin2x +9cos2x  We have to verify y = 7sin2x +9cos2x is a solution of y"+4y = 0

Q: Find the general solution 6. y"+4y' = sec2x Solution 6. y=c, +c, cos 2x+c, sin 2x+ 16 sin 2x -In(sec…

A: Given differential equation is y'''+4y'=sec2x We have to find the solution of the given differential…

Q: Suppose that y1=e^x andy2=e^-x are two solutions of a homogeneous linear DE. Explain why y3=cosh x…

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Q: y" - 5y'=x-2, when x = 0, y = 0, y = 2

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Q: (2 - 3 sin 30 + y) dy- (9y cos 3p- p+1) do 0, y (0) = 2 Dy+4y-6y sin 3p+ q-20= 12 O y-y+9y cos 30- p…

A: We have to find

Q: Rewrite y" - 2y + y² = cos x as two first-order equations and then use Euler's method to integrate…

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Q: Find the general solution Solution 8. y= c, +c, cos 2x+c, sin 2x- 7 e* cos 2x+ 85 6. e* sin 2x 85 8.…

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Q: Solve the exact DE (2xy³ + cosx tan y +2 sin x)dx + (3x²y² +sin x sec² y-3 csc y cot y)dy = 0 (1)…

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Q: Find the particular solution using the initial condition. y' sin(2y) - cos x = 0, y() = 0 O y = cos…

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Q: Find the solution of the equation zxx + zyy =e-xcos(y) which tends to zero as x-> ∞ and has the…

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Q: Solve the initial value DE y - ytanz = sinx, y(o) = 1 5-Cos 2x 5-Cos 3x 5-Cos 2x Cos 2x A) y = B) y…

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Q: Find the general solution of the nonhomogeneous equation y " - 3 y "+4 y ' – 12y =e + 2 1 3* + C,…

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Q: The general solution of y"+ 16y3cost is: Select one: а. y = C, cos(4t) + C, sin(4t) + tcost 15 b. y…

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Q: Show that an implicit solution of 2x sin?(y) dx - (x2 + 17) cos(y) dy = 0 is given by In(x? + 17) +…

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Q: Find the general solution of y''+ y =1/cos x

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Q: 44. First verify by substitution that y (x) =x=1/2 cosx is one solution (for x > 0) of Bessel's…

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Q: 2. Find the solution set on [0, 2n). sin²(x) + cos² (;) – : -2 =0

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Q: The general solution of y" + 16y = cost is: Select one: а. v = C,cos(4t) + C,sin(4t) + 1 -cost 15 b.…

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