19. Solve the following differential equa- tions using classical methods. Assume zero initial conditions. [Review] dx a. +7x = 5 cos 2t dt d²x dx b. d1² + 6 + 8x = 5 sin 3t dt d²x dx C. dt² +8+ 25x = 10u(t) dt

Q: Use perturbation method to linearize the following nonlinear differential equation: Ý = Xsinê —…

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Q: c). i. Find the general solution to this homogeneous equation using the auxiliary equation method…

A: We will use the basic knowledge of differential equations and methods for solving them to answer…

Q: - x dy = 0

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Q: 3. (D'+ 9) у -D0 %3| Ans. y=c, sin 3x+c, cos3x

A: See below the answer and explanation

Q: 4. Evaluate + tyt - 1j+t sin at k) dt

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Q: Q.3 ) Solve the following D.Es: 1. 4d²y d¡ 2 +y =0. when t=0, y=1 and dt dy :-2. dt 2. xy =(1–x 2)y…

A: The solution to the given differential equations is explained below.

Q: dy Q1: Solve the DE x3 dx3 +x = x Inx cos(2lnx) by using inverse dx operator method.

A: Given differential equation is .....1 Its solution is given by yx=C.S + P.I ; where C.S is…

Q: Q1: Find 1) e (3 + e6t)2 2) l {e¬3t (t + 1)²} 3) е sin 3x dx dt 4) l (3t5) 5) e (est + cos 3t)

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Q: Find dy/dt. 11) y = (ecost/9)4 A) cos e4 cos(t/9) B) sin e3 cos(t/9) e4 cos(t/9) D) - (esin(/9)3

A: Use the chain rule of derivative and simplify.

Q: S(2) = e- f(2): cos 2ry+ie sin 2ry 2. Find the cauchy-riemann equations of rau du dv dv ləx'əy'əx'…

A: Find partial derivative with respect to x and y.  Comparing real and Imaginary part find u and v.

Q: dz Calculate for z = 4x² + 3y², x = sin(t), y = cos(t) dt

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Q: PART 1: State the characteristics (order, degree, type) of the given DE. 1. (1-x)y" - 4xy' + 5y =…

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Q: Q3: Show that b. I — = ƒ‰e¯¹8(2t − 2). dt = ½-½ 2e C. L²u(t)dt = = [cosnt. 8(t − 2) + 38(t+1) +…

A: We have to prove the given statement.     According to our guidelines we can solve only three…

Q: find dy/dt.

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Q: đã cesitty) tanh (sin4)= in 34 yech (z)

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Q: Linearize 8.12 about dt 2 ot/A x = J + 2 ds + co5x = 0 dt

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Q: 4. Shown at right is the slope field for which differential equation? dy A. dx dy dx dy dx D. dx B.…

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Q: 3. Let z = x?y + 3xy+ where x = sin 2f and y cos t. Use the chain rule to dz find when t = 0. dt

A: As indicated in the question, we will make use of chain rule of differentiation. Recall that the…

Q: Solve the D.E [y(++csy)]dx + [x+Inx-xSiny] dy-o

A: Solve de

Q: Q1: Find 1) e (3 + e6t)2 2) l {e-3t(t + 1)²} t } 3) e- sin 3x dx dt 0,

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Q: 3. Solve the IVP: siny(x + siny)+2x²cosy y'=0; y(-1)= π/2 (Subst. first and then Bernoulli's)

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Q: 1. y = √2x +7 2. y = √7+√√3x + 1 3. y Arctan√1-x²

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Q: = dx 1. If 2y + siny = x¹ + 4x³ + (2π − 5), show that dy 16 when x = 1.

A: If draw the graph of Sin(y)= 2(π-y) , then we get only solution y= π

Q: Q1: Find 1) l (3 + e6t)2 2) e {e-3t(t + 1)²}

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Q: - (7- dy sin2x ) dx = 0 y y

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Q: o(e) = La t -Va V1 + t²

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Q: 5. ex+ydx = dy χ

A: “Since you have posted multiple questions, we will provide the solution only to the first question…

Q: d. Evaluate dx dt (t2 +2t) -1

A: We use the Leibnitz rule of differentiation under integral sign to solve the given problem.

Q: Find dy/dt. 11) y= cos(N&t + 12) A) -sin(Na 12) B) 2N8t + 12 sin(&t • 12) 4 C) 8t + 12 4. D) -sin…

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Q: Calculate. for z = 4x² + 3y², x = sin(t), y = cos(t)

A: We will use chain rule for total derivative  If z is a function of x,y . Where as  x and y are…

Q: , find dy/dx. х • 7x² V2 + cos³t dt 126. y 125. y = V2 + cos³t dt 128. y 127. y = dt 12 + 1 dt 3 + A

A: Hey, since there are multiple questions posted, we will answer the first question. If you want any…

Q: Q1: Find 1) l (3 + e6t)2 2) l {e¬3t (t + 1)²} 3) е sin 3x dx dt 0. 0. 4) l (3t5) 5) l (e5t + cos 3t)

A: We can solve these problems by Laplace transforms.

Q: y(4) + 2y" + y" + 2y' = 4x2 3xe 2x + 2 cos 8x |

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Q: Solve the following DE: [3sin (y) — 5x ]dx + 2x²cot(y) dy=0 Ox²[sin (y) - 2x]³=C'sin³(y) Oy³[sin(y)…

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