The general solution of 4y" + 4y' + y = 0 is y(x) = (A) ce-2² cos(x) + c2 e¯2z sin(x) (B) c e2 + C2c e2 (C) ce-2z + c2 e²z (D) ce+ c2xe (E) None

Q: C₁ and C₂ are constants. For the DE y" + 12y' + 35y = sinx, (a) the complementary function is Yı(x)…

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Q: (b) у" — 2у + у 3 еt sin(z)

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Q: S[y] given by y = cosh æ + B sinhx, 0 0,

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Q: The solution of (e +2ay) daæ + (2 cos 2y+ 2x?y) dy is given by (A) e" + a?y² + cos 2y = c (B) e +…

A: The given equation is; (ex + 2xy2) dx + (2cos2y + 2x2y)

Q: The general solution of y" + y = e + 5e2* is y = ei (A cos (*) + B sin )) + Ce-" + 응e2x 2 () V5z y =…

A: Given that  y"'+y=e^(-x)+5e^(2x) To find the general solution

Q: x*y"+xy'+(x? y=x cos x 2. Show that is a solution of the equation

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Q: The solution of (e+2xy?) dx + (2 cos 2y + 2x?y) dy is given by (A) e + x?y? + cos 2y = c (B) e +…

A: To find The solution of the given differential equation.

Q: What is the general solution of the given equation, cos(x + y) + 2x + (cos(x + y) + 4y)y' = 0 OA…

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Q: If f(x) = cos(3r), then f(77)(x) %3D (A) 37 cos(3æ) (B) 377 sin(3x) (C) –37 cos(3æ) (D) -377 sin(3x)

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Q: The solution of (e + 2xy?) dx + (2 cos 2y + 2x y) dy is given by (A) e +x'y² + cos 2y = c (B) e"…

A: Given D.E is (ex + 2xy2) dx + (2cos 2y+2x2y) dy = 0     To find the solution of the given D.E .

Q: The general solution of 4y" + 4y' + y = 0 is y(x) = %3D (A) c1e-2¤ cos(x) + c2 e¯2ª sin(x) (B) c1…

A: solutionGiven 4y"+4y'+y=0to solve this we solve its auxillary equationwe get its auxillary…

Q: Find x and y for which the following equation is satisfied: x+2 = - 5+i i-5

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Q: Just C please explain in detail.

A: Given- Consider a3xy''' + a2xy'' + a1xy' = 0 To find- Suppose a3x = k3x3, a2x = k2x2, and a1x = k1x.…

Q: Solvecos (2) O a. O b. 2 с. d. y cos Y I - [2 in (2) + co. (:)]* - = 0 dz y sin () = c C = сх ysin…

A: Given differential equation is yxcosyx-xysinyx+cosyxdydx=0       (1) Simplifying (1), we get…

Q: Match the graphs with their parametric equations. I O (a) x=4-t+2, y = ² O (b)x= 2 - 3t, y = √t O…

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Q: on of y" – 2y' + 2y =

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Q: dy cos?x = -(tan x)y ;y(0) = -1 b) Solve %3D dx

A: Given that: dydx-cos2x=-(tanx)y; y(0)=-1

Q: a) 12 Q.7) To write the power series £=3 4m as the form -4m a) m - 1 we must shift m to become : d)…

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Q: (D³ + 3D + 4D³ + 12D²) y = 32 cos (2x) +3e3 – 16 sin (2) -

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Q: f(x) = 2) f(x) = 1+2 cos 2x, 3) f(x) = 1-2 cos x %3D 2

A: (1)   Let the function be,   f(x)=x-1x   Find the domain of the functionf(x)=x-1x Here, the function…

Q: The special solution to the equation * (D²-3D+4)y(x)= 4sin(2x) Y,(x) = Excos(2x) у, (х) cos(2x) -…

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Q: "+2y(y)² = 0 =1^²)={1^²/ LV=X+C₂ y(x) = c₂e¹1* - 1 . (C₂-y)² + x² = C₁ :C. -In(c 2) 71

A: Given differential equation

Q: The general solution of y" + 4y' = 12 can %3D be written as (A) y = c1+ c2e¬2= + c3e2 + 3x (B) y=…

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Q: Find the general solution of (2x + y cos (xy))dx + x cos (xy) dy= 0 Show your solutions on a…

A: Solution

Q: Q.1) The general solution of the equation e' cos , is:

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Q: Solve

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Q: The solution of у" + у 3D 0, у(0) — 0, у'(0) — 1 is y(a) = (A) cos x (B) sin x (С) 1 — е ӕ (D) 1– eª…

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Q: • If y = cos x2 + x² then y(4) = 8x? sin x² + 0 TO F

A: Topic- Derivative

Q: (a) a²y + y sin r = xy. (b) y = x³y - 2y³. (c) y = e²-2y (d) y'= x² + y² xy

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Q: Find LT of (i) e(2 cos 5t – 3 sin 5t) 3t (ii) e²ª cos? t (iii) e* sin 2t cos t

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Q: (a) (i) Use the substitution sin(u) = x + 3 to show that dx 12x + 7 -1 (x+3) V-2x² – 12x+7+c. sin -…

A: As per company guideline we are supposed to answer only one question with maximum 3 sub parts at a…

Q: Solve the equation y' + a = eax +)csc(ax+y), where a is a real number Select one: a. e-(x…

A: The differential equation is given as y'+a = e(ax+y)csc(ax+y)                          (1) Let ax+y…

Q: Solve the general solution y4 + 2y" + y = x² sin x

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Q: c) y(x) = c, + cz + Acos3x + Bsin3x Q.6) The singular point (s) of (x² + 4)y" – x y' + 4y = 0 , is…

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Q: The general solution of 4y"+4y' +y = 0 is ()%3D

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Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.