dr = x – y +t dt dy =エ+3y +t+1 dt (20, yo) = (-4, 5)

Q: 3. Find (6-+- vē)dt Vy 4. Find S- dy (4-yの?

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

A: We need to solve the given differential equations using Laplace transformation. For (a),

Q: d²y dy 4+ 5y = t dt dt2 dy y(0) = 0 (0) = 1 dt

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Q: Consider a disease where immunity is lost. On average, after n days, a recovered person becomes…

A: Let t be the time ,which is an independent variable (measured in days). We have to take two related…

Q: d²x dx 2 + 10x = e2t x(0) = 0, x'(0) = 1 %3D - dt2 dt

A: Given differential equation is d2xdt2−2dxdt+10x=e2t. and x0=0, x'0=1 Write the auxiliary equation…

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: [(x²-y²)²] x+y -2 LEK 1J0 du dt

A: We have to find value of given double Integral.

Q: 2) t (y-1) dt +y(t+1)dly=0 31 хчуу! -2y =. 41 yan- x lnn dy ==

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Q: * = x- 2y+ 2z = -2x+y– 2z dt dy dt E = 2x – 2y+ z dt

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Q: A mass-spring system is modelled by the differential equation u" + 16 u = 0 , and the motion starts…

A: Given that u''+16u=0   with   u0=7   and  u'0=4. Its auxiliary equation is m2+16=0. Solve as…

Q: Solve IVP: dx x + Y, (0) = 0 dt dy 4x + Y, y (0) = 3. dt

A: Since you have posted multiple question we are supposed to give solution of first one only ...kindly…

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: Find the integrating factor of : zydz = (x² + 2y²) dy 1 a. µ 2у3

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Q: (dx — Зх — 2у dt dy 3D —х + 3у — 2z dt dz = -y + 3z dt %D (λ1, λ = 3, λ5)

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Q: dx dy -- x - 2y = 16te', 2x – dt - 2y = 0, x(0) = 4, y(0) = 0 dt

A: We will find out the required solution

Q: 4.Solve the pair of simultaneous equations dx =xy-t, x(0)=1 dt dy = x+t, y(0) = 0 dt From t=0 to…

A: You don't mention any method by which we can solve, so i use simple Iteration method Euler's Method

Q: What is the differential equation of the orthogonal trajectories of x3 = Cy? (1) Зxdx + 2уdy — 0 (2)…

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Q: integrate dy/(sb - smy-bny-nmy^2

A: SOLUTION-

Q: dx dy - x - 2y = 16te', 2x – dt - 2y = 0, x(0) = 4, y(0) = 0 dt

A:

Q: dx dy - x – 2y = 16te', 2x - dt - 2y = 0, x(0) = 4, y(0) = 0 dt

A: The given differential equations are                                  dxdt-x-2y=16tet ..............…

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: dy 2х dx - y = 6e3t, dt dt dy 3x + dt dx - 3y = 6e3t; | dt x(0) = 3, У (0) 3 0.

A: Given, dxdt-2x-dydt-y=6e3t2dxdt-3x+dydt-3y=6e3t, x0=0, y0=0   We use the Laplace transforms…

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

A:

Q: Show that if

A: To Determine: show that      dydt=ky1-y Given: we have y=11+be-kt Explanation: we have  y=11+be-kt…

Q: 1 y' = 1– sint - y(t)dt, y(0) = 0 0,

A: Given the equation y' = 1-sin(t) -∫01y(t)dt. Initially, we integrate both sides of this equation…

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

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Q: Determine the Integrating factor of the DE: y (x³e*y y) dx + x (y + x³e*y) dy 3 1

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Q: 1. Write down the system of differential equations for the gradient flow associated to V (x, y) : xy…

A:

Q: 1/4 sec2(t) dt J-x/4

A: Given: I=∫-π4π4sec2tdt

Q: Integrate  zex^2 + y^2  over the cylinder  x2 + y2 ≤ 25, 2 ≤ z ≤ 5.

A: Integrate zex^2 + y^2 over the cylinder x2 + y2 ≤ 25, 2 ≤ z ≤ 5 as follows.Here, x2 + y2 = 25 and…

Q: = 4x - 2y + 2U(t – 1) dt dy 3x - y + U(t – 1) dt x(0) = 0, y(0) ])•(C ])•(_ x(t) = | ) «(-[ y(t) :

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Q: 13. dy/dt = y²(1-y)², -∞ <yo <∞

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Q: dx x + y + 1 dt dy x + y +1 dt

A: Given dxdt = x+y+1                          (1)dydt = x+y+1                          (2) Then dxdt =…

Q: Find all the critical points (equilibrium solutions) of dx dy = y+ 5xy. dt dt

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Q: Solve y(1): dy/dt + x = 1; dx/dt-y + 4e¹ = 0; x(0)=0 and y(0)=0.

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Q: Solve the IVP dy/dt + 2(t + 1)y^2 = 0, y(0) = −1/8

A: To solve the IVP dy/dt +2(t+1)y²=0, y(0)=-1/8

Q: dy - 4 - 5y = dy -3t sin(4t) ; y (0) = 3, y (0) = 10 dt2

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Q: Create a slope field of the differential equation dy cos(t) + cos(y) dt and draw solutions…

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Q: The order and degree of the partial differential equation respectively 6 9. dz + sin x xy is ду О…

A: Consider the given partial differential equation. Order of the partial differential equation is the…

Q: d²y 2 dy +5y=0 dt dt2 y (0)=2 y'(0)=-4

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Q: (2) An integrating factor of (xy³ + y)dx + 2(x²y² + x +y*)dy = 0 is (a) y (b () (d) 2xy

A: We need to find an integrating factor of xy3+ydx+2x2y2+x+y4dy=0 Now, a differential equation of the…

Q: Solve simultaneous equation dx/dt=2x+3y , dy/dt=x+4y , x=-3 , y=1

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Q: d²y 5 dy +6y= e7t dt dt2 y (0)=0 y'(0)=2

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Q: Find the integrating factor of y(2x - y + 1)dx + x(3x – 4y + 3)dy = 0 Oy? 2x О ху Oy

A: See the details solution in below

Q: Create a slope field of the differential equation dy = cos(t) + cos(y) dt and draw solutions…

A: Given: dydt=cos(t)+cos(y) To find: Slope field To sketch: The solutions corresponding to y(0)=0.5,…

Q: 3. Integrate! 12e-0.21 а) -dt b) 6r 3,2 Se041 dr dx c) f- x. V1+ In 3x?

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Q: 4. (4y+ 21 - 5)dt +(6y+41 –1)dy = 0, y(-1)= 2 cs

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Q: d²x dx + 4- + 5x – 10 = 0, when t = 0, x = 0,x = 0 dt2 dt

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Q: Solve y(1): dy/dt + x = 1; dx/dt -y + 4et = 0; x(0)=0 and y(0)=0. 6.33 4.89 O 7.10 3.51 O 1.80

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