D’(D² – 4)y = 3x+ 2e¬3* | y = 3x + 2e¬3x m° – 5 - 4m³ = 0 ® m' (m2 – 4) = 3x+2e-3* D (D² - 4) = 0 3 |

Q: dy If y = (t + 6t + 4) (3t2 + 4), find dt dy %3D dt

A: it is required to find the derivative.

Q: cos (2t + ) dt e21–3 %3D 4 -3 4 64e3 7.

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Q: 1. d'y_dy - 42 + y =r²-2t +3 dr dt 2. y"-7y'=(2x-1)sin 2x 3. y'-5y=xe" – xe*

A:

Q: dy dr 1. cos(r + y) y(0) = 2. (4ry + 3x²)dx + (2y + 2r²) = 0, y(0) = –2

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Q: Solve simultaneous equation dx/dt=x+y , dy/dt=4x+y , t=0 , x=2 , y=5

A: First I have written the differential equation into operator form and then reduce it into linear…

Q: dx 2х — dt dy – y = 6e3t, dt. dx 2 dt dy 3x + dt - 3y = 6e3t; %3D x(0) = 3, У (0) — 0. %3D

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

Q: d²y dy dt + 81y = 0, y(0) = 9, y' (0) = 3 + 18- %3D %3D dt?

A:

Q: dy If y = (t + 2t + 8) (6t² + 6), find %3D dt dy dt

A: The given question can be solved as shown in step2.

Q: dz 2. Given z = 4x2 + y²,x = sin t, y = t², find- %3D dt

A:

Q: dx dy (a) dt di -y = 6e3t, 2 dt -3x +-3y = 6e3t; dt x(0) = 3, y(0) = 0.

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

Q: b- Yt dt + dBt dY; 1-t

A:

Q: d y dy 14. dt2 +2, + y= 2 cos 2t dt У (0) —D у (0) — 0

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Q: dy The solution of (1 + y?) + (t – elan-ty Y = 0 is: %3D dt Select one: a. 1 t = etan-ly e2tan-ly O…

A: We have to choose the correct answer from the given condition according to the given condition

Q: Solve the following initial value problems using Laplace Transforms:

A: a.) The given initial value problem is,

Q: obtain the particular solutions satisfying the indicated conditions: dx/y=(25-x^2)^-1/2dy; y(0)=1

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Q: Q3 (d^2 y)/(dx^2) - 2dy/dx of Undetermined Coefficient) 20e^(-x) cos(x), y(0) = 0 = y'(0) (Use…

A: we have to solve given differential equation by using method of undetermined coefficient

Q: (2y-x)(dy/dx) = 2x + y, given that y = 3 and  when x = 2 Homogeneous equations

A: Solve the following problem by substitution.

Q: C/ Answer two only: dy dy 1- y= eV1+5x? the dx 3- y= 2r° +3 , x =, he .(using chain rule). dx dy 2-…

A:

Q: Solve the I.V.P: dy = 6y²x; y(1) = 6y?r; %3D dx Oy 1 372-8 1 Oy = 8-3z2 Oy 1 8+3z? Oy = 1 !! 8-3z

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Q: 4 J4- y ktx dy S[S( x, y) dA = [] 3 R 0 2- 2 2

A: Consider the given expression, ∬Rfx,ydA=∫04∫2-y24-yx2-x33dxdy This suggests that the region spans…

Q: Find the solution of dy dy +2 - 3y = 2e2", y (0) = 0, y' (0) = 0 dt2 dt

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

Q: b- dy +2y=0; y=1 at t=0, y(0)=1 dt

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Q: J(2t-3)-e-t²,3t i. 2t – dt 3 2vlnx dx . ii. X 2 iii. (2y-3]12 kdy.

A:

Q: w = In(x²+y² +z²) x = cost y = sint z = 4E

A: w=lnx2+y2+z2, where x=cost, y=sint, and z=4t. Find dwdt.

Q: d² y dt² + 3 dy dt +2y(t) = 2e²¹ ; y(0)=0_

A:

Q: b. y = cosh(arctan 3x) C. y = 4a/ cosh a d²y d. for x = 4v2t2 + a, y = a² – t² dx2 %3| -

A: Given functions are  b) y=cosh(arctan3x) c) y=4acosha d) d2ydx2 for x=42t2+a , y=a2-t2

Q: d² y dy } +24% +y=sinh3t – 5 cosh3t ; y(0) = -2, dt² dt y (0) = 5

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Q: solve using ODE from t=0 to 2 when y(0)=1 dy/dt= yt^3 - 1.5y

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Q: - (t/z? + y² – y) at dt + (y/t² – y² – t) dy = 0; when t 3,y = 4

A: Answer is  ty=3(t2+y2)3/2-363

Q: dy Find a solution of x dx y2 - y that passes through the indicated points. (a) (0, 1) y = | 0

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Q: d²s ds + dt 4t + 2cost where s = 0, ds/dt = 0, t= 0 dt2

A:

Q: The two functions x(t) and y(t) satisfy the simultaneous equations dx/dt - 2y = -sin(t), dy/dt + 2x…

A: Given: dx/dt - 2y = -sin(t), dy/dt + 2x = 5cos(t)

Q: 4d'y dt? dy -8y= 8e, find the solution dt a) Using the Method of Variation of Parameters

A: Given differential equation is 4d2ydt2−4dydt−8y=8e−t....1 We have find the general solution by using…

Q: %3D y"(t) = 4y(t) – e-tU (t – 1), y(0) = y'(0) = 0.

A: Solution

Q: Evaluate: J-1)–1) dy 0-my-1-등u-1)" + 즐피 ++ 11-arctan(Y )+c arctan () +c V3(2y+1) O-m-- 1³ + }n² +…

A:

Q: 2 In(t) and y=4 t2 then find %3D %3D dy dx d'y dx2

A:

Q: z = √xy, dz dt t², y = -t² then 2 2 2t²) =?

A: We have to choose the correct option from the given options according to the given information

Q: LLL- (x+ y+ z)dydxdz. -1 J-1 J-1 |

A:

Q: 3e2º sec 20 dy determine de Given y = V(0-2)

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Q: what is the equilibrium of dy/dx = y - sqrt(y) when y >0

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Q: ds where t+s = 2s . dt Find %3D 6.

A: t+s=2s

Q: What is the interpretation of Vx'(t)2 + y'(t)² for a particle following the trajectory (x(t), y(t))?

A: The particle is following the trajectory (x(t), y(t)). Velocity across x axis = Vx = Rate of change…

Q: dy dæ at x = 2 if y = 3x + 5 and dt Find - 2. %3D %3D - dt dy %3D dt

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Q: dx dy Explain your solution to the problem: = x + 3y – 2t², 3x +y+t.+ 5 dt ||

A: Given the system of differential equations:              dxdt=x+3y-2t2                  ......…

Q: •ý -2ý +y= ě sinx %3D Ans: y=ě +2xě - ě sinx • ý -uý ruy = 12 /* %3D e 2X 2 ZX .2 +C2 X e + 20

A: As per our guideline we are allowed to do 1 question at a time. Please post other questions next…

Q: dy Find -5 y%3D(2+cos4t) dy dt

A:

Q: 4) Solve d²y + 4y = 2e¬t %3D dt2 Where y(0) = y(0) = 0 %D

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Q: Q16 3⁰ 3t+2 a) 1 b) J dt dr cos² r√5 + tanz dt (3-5t)²

A: see below the answer and calculation

Q: 5.Express this model of an electric circuit d² y dy +6¹ +5y=sin10t, y(0)= 0, y'(0) = 1 dt² dt As a…

A: First I have introduced two functions and then find pair of first order differential to the given…