In each of Problems 19 through 22, The given differential equation Descr

Q: 41. y' + (1/t)y= 3 cos 2t, t> 0

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Q: Problem 11 §4.7, Exercise 5. Solve the initial value problem X = CX where Xo = e1 given that (a)…

A: Given that the initial value problem is  X.=CX where trC=3 and C is a symmetric matrix. Hence C is…

Q: 7. y' = (4 - ty)/(1+ y²)

A: We are given a differential equation  y'=4-ty1+Y2.............(1) We need to draw the slope field…

Q: a) x³y" - x²y" + 2xy' - 2y = 0, x > 0, y(1) = -1, y'(1) = -3, y" (1) = 1

A: (a) To Solve: x3y'''-x2y''+2xy'-2y=0, x>0, y1=-1, y'1=-3, y''1=1   (b) To Solve:…

Q: dt + sin(t + y) = sin t

A: The given equation                     d2ydt2+sin(t+y)=sint second-order non-linear

Q: y(Inx – Iny) dx = (xln.x – xlny – y) dy |

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Q: d²x dt² - x=0, x(0)=0, x(1) = 1

A: We have to find the solution of the differential equation.

Q: In each of Problems 34 through 37, construct a first order linear differential equation whose…

A: To find- Construct a first order linear differential equation whose solutions have the required…

Q: (1 – xy)-2dx + [y? + x²(1 – xy)-²]dy = 0 (y – cos?x)dx + cos x dy = 0 + Ri = E, where L, R, and E…

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Q: y(x2 + y? – 1)dx + x(x² + y² + 1)dy = 0 У (2x2 — ху + 1)dx + (х — у)dy %3D 0 x2 + y2 dy 1 dx…

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Q: 7. yy' = (x + xy²)e²²

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Q: d'y 3-d + dt + dy + +y=1 de

A: Given differential equation is ,    d4ydt4+d3ydt3+d2ydt2+dydt+y = 1 (.)  Order of a differential…

Q: 3. xcos(xy)+ e' In y c COS

A: As per our guideline we are supposed to answer only one question .kindly repost other question. The…

Q: dy + y = 2ry?e" 3. dz

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Q: 23- y" - 2y + y = 0; y₁(t) = et, y₂(t) = tet

A: 23. Given y''-2y'+y=0   Also given y1t= et,  y2t=t et   To verify: the functions y1, y2 are…

Q: 29. y" – 4 y' + 4 y = 2 e2'; particular solution ? e?'

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Q: ). y" + y = sec t, 0<t</2; y = (cos t) In cos t+tsin t

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Q: xy" - y' + 4x y= 0, x> 0; y,(x) = = sin x

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Q: In each of Problems 21 through 24, determine the values of r for which the given differential…

A: Given y"+y'-6y=0

Q: 4. f(t)=e¹+7. 5. f(t)= test. 6. f(t) = tcost. 7. f(t) = t sint. 8. f(t) = et sint.

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Q: 15- " + ý +4y=2 sinh t y". Hint: sinh t = (et - e-t)/2

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Q: . (y+x) dx-x dy = 0

A: As per our guidelines, we are supposed to answer only one question. Kindly repost other question as…

Q: 17. 2t²y" + 3ty' — y=0, t>0; y₁(t) = t¹/², y₂(t) = t-¹

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Q: B. Non-Exact 1. (y-y) dx + x dy = 0 2. (4xy + y') dx -2(x2-y) dy = 0 3. Y' = (y +1)/x 4. (y +x) dx-x…

A: As per our guidelines we are supposed to answer only first asked question.kindly repost the other…

Q: 6. x' = 2 (³²3 −12) x + (-1). -2 e²

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