Question 1 The y solution of the system is y=e' (c cos2/2t+c2 sin2/2 t)-1 y=e" (c, cos/2 t +c2 sin/2 t)+1 y=e" (c, cos2/2 t+c2 sin2/2 t)+1 y=e' (c, cos/2 t +c2 sin/2 t)-1

Q: What is an equation for the cosine graph shown below? +10 -9 8 -135 -90 Oy 8 cos(0-135") +4 Oy 4…

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Q: Find the solution. (D5 - 2D3 - 2D2- 3D - 2)y = 0. -3x y = (c,+c,x)e-*+c;e-+e*(c,cosx+c gsinxr) -2x A…

A: Given differential equation is (D5-2D3-2D2-3D-2)y = 0

Q: Example 7: Find the solution of y + 2ý + 4y =x cos 3x The chr. Eq. is r? + 2r + 4 = 0 -bt vb2 - 4ac…

A: “Since you have asked multiple question, we will solve the first question for you. If youwant any…

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: عو + Y¹" + 3 Y" + Y' + 22 = 0 general Solution : Y = C₁ cos ax + C₂ Sinba + exp(-22) (C₂ Cos √ 1+1…

A: The auxiliary equation

Q: Solve for the general solution of the equation: y" +4y=-x+4e², Ⓒy=c,cos2x+c sin2x -0.8x+0.25e…

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Q: y" + 4y = 2 sin 3x + 3 cos 2x Find the solution y(x)

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

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: ind positive constants b and n, such that 3n + 2 n.

A: Finding the values of b and no

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: O y(1) = c, e*" + C,e For each set of solutions below, match the solutions to the general s Prompts…

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Q: Consider the equation 4y" + by' + cy = 0 the constants b,c,m,n are real and different from zero, the…

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Q: |(5e" + 5x4 =. + 9 cos x)dx 5et + x + 9 sin x + c 5ea + x + 9 cos x + c 5e + x³ – 9 sin x + c O et –…

A: Need to find integration

Q: y" + 4y + 5y = 50t, y(0) = 5, y'(0) D a.e-2t (13 cost + 11 sin t) + 10t² - 8 b.e-2t (13 sint + 11…

A: The given IVP

Q: The general solution of (D²+2D +1)(D²+4)y=0 is A y=(C,+Cx)e+C,cos2r + C ,sin2r B…

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Q: on of y" – 2y' + 2y =

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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: Find y @) y ² y's SX-2 Sin (x) b) 2 Y = 2 cos (x)-x

A: To find the derivative each of the following functions. (a) y=5x-2 sinx (b) y=2 cosx-x2

Q: The general solution of y" + 4y' = 8, can be written as (A) y = c1 + c2e¯2« + c3e²a + 3x (B) y= c1 +…

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Q: y" + 8y' + 25y 2t-e-4t + 5 cos 3t

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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: Which of the following is true? A) y "'- 4y' + 4y = 0 The general solution : y=c₁e²x+c xe ²x 2x B)…

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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: Solve: (2x cosy + 3x y) dæ + (x – a? sin y – y) dy = 0 O 2x cos y + 2x2y-y = C O x3 cos y + x?y-y =…

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Q: x - ; )* ( sin 2t X' |X + 4 2 \2 cos 2t)

A: We have to solve the system of equations.

Q: The system x' = cos(t)x+ sin(t)y y' = cos(t)x - sin(t)y is linear.

A:

Q: - (D' - 4)y = x'e"

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Q: - فم( (x² – 4)²dx 6. -2 10x4 x3 1 + 15Vx3 – 7) dx 7. 2 3 dx 2x° + x4 8. 1 | (2x + 1)(x – 1) dæ - 9.…

A:

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

A:

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.