dy dy 6. = y³, y(0) = –2 dt 5. = y³, y(0) = 0 dt dy 7. dt = t(y² + 4), y(0) = 2 dy 8. dt 1+ y? y(0) = Ve – 1

Q: dx 8х — 9у dt dy = x + 2y x(0) = 2 y(0) = 1 - dt

A: The solution is given as

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

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Q: 8. Solve: dx dt =x-4; dy dt = = 4y+t²; t = 0; x = 1; y = −3

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Q: d?x ax dx ÷+ 9x = 0, when x(0) = 1 and (0) = 0 dt2 dt dt

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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: 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: 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: Let y = y(t) be the solution to the initial value problem dy – y = e' cos t; y(0} = 1. dt Find the…

A: Given that y=y(t) be the solution to the initial value problem  To find the value of y(pi)

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: dx? dy = y(t) - dt2 dt dz x(t) + dt dy dx z(t) = 0 dt dx + 3x(t) + 4y(t) + 3z(t) = 0 dt dt when x…

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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: dy = 3. dt dz at (x, y) = (3, 1) and z² = x² + y² if dx = 1 and dt Find dz Preview dt

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

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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: 1. Solve for x(t) and y(t), given that x(0)=4 and y(0)=3 dy - y = 0 dx + x + 4y dt — 10%; х - | dt

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Q: y = tx2 + tx dy Find dx dy dx + 2tx * dy Find dt dy dt II

A: Given that y=tx2+t4x We have to find dydx  and dydt dydx is the derivative of y with respect to x…

Q: dy a) +7y = 5cos2t Assume zero initial conditions. dt d'y a) dt? dy +y=8(t-2) where y(0)=1 and…

A: Some of the properties of Laplace transformation L-11s-a=eat  Lu(t-c)=e-css Lδ(t-c)=e-cs…

Q: d?x dy -y = 0, dt? dt dx 2- dt dz +- z = 0, dt dx dy + 3x + dt -4y+ 3z 0; dt dx x(0) = 0, (0) = = 1,…

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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: dx If x2+y2+z2 = 9, dt dy = 6, find dz when (x, y, z) = (2,2,1). dt 4, dt dz dt when (x, y, z) =…

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Q: The DE dy/dt = µy – oy², µ > 0 and o > 0 occurs in the study of population dynamics. It has general…

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

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Q: 1. Solve for x(t) and y(t), given that x(0)=4 and y(0)=3 dy dx + x + 4y = 10; æ dt - y = 0 dt

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Q: 1. Solve the DE as follows: d'y dy +3- 2 dt +2y= 24 y(0) = 10 and y'(0) = 0 dt

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

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Q: - y"+2y'-3y= 32e*; y'(0) =12, y(0) = 0 dy +2y 0; y=1 at t=0, y(0) = 1 dt dy +2y = cost; y(0) = 0 dt…

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Q: dx 3x – 5y dx = 3x – y + 2z +t-1 dt dt (a) dy = 4x + 8y dt dy (b) 2x -z- 3t2 dt dz x+y+z+t? dt

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Q: 2. Find dy/dx a) y = dt, x> 0

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Q: (y')² – 3yy' + xy = 0 12 +y = x \dx², S + (S + = 0 dt² dt² dy x*y" + xy" = ex ds t2 \dt², () - t=1 –…

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Q: 3. 4 - y = 5 with zero initial conditions (i.e. y(0) = dy(0) dt dy(0) fy0) = 0) di IP Answer: y(t) =…

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Q: 1. dy ==2(y+1);=3y-x+e³; t=0; x = 1;y=1 dt dx dt

A: SOLUTION: Given: dxdt=2(y+1)   ;  t=0;x=1;y=1dydt=3y-x+e-3t

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: dx + 2x = dt dy + 10 cos t, dt ay + 2y = 4e-2t – dt 业 da if x = dt rstem

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Q: 5. Solve dy+dy =5 with y"(0) = 0, y'(0) = 2, dt dt У (0) %3D0

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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: he given initial-value problem. dx = y - 1 dt %3D dy -6x + 2y dt x(0) = 0, y(0) = 0 0, у (0) %3D 0

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Q: e. dt2 d²y dy + 4y = 8t – 10, y(0) = 1, y'(0) = 7 dt f. 3- dy 3– 2 - y = 2y – 1, y(0) = 7,y'(0) = 2…

A: Since you have posted multiple question and according to guidelines we will solve only one question.…

Q: What is the differential equation of the orthogonal trajectories of х3 — Зху — уз %3 С? (1) (x +…

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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: If X+y = x-y x2. -y2 and dx/dt = 12, then what is dy/dt when x = 1 and y = 0? О 12 O -12 12

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

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Q: 3. - y = 5 with zero initial conditions (i.e. y(0) dy(0) = dt dºy(0) 'y(0) -0) %3D %3D Answer: y(t)…

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Q: d²y dx² -3 dy dt 4y = 3 sin x given y(0) ) = 0 and y'(0) = 0

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Q: 3 * (dx)/(dt) + (dy)/(dt) + 2x = 1, (dx)/(dt) + 4 * (dy)/(dt) + 3y = 0  Given x = 3 y = 0 when t =…

A: As per the question we are given the following system of differential equations : 3x'(t) + y'(t) +…

Q: 9. dx/dt = −(x − y)(6 — x − y), dy/dt=x(4+y)

A: Given that, dxdt=-x-y6-x-ydydt=x4+y We have to determine all critical points of the system of…

Q: 3. 4 - y = 5 with zero initial conditions (i.e. y(0) = dy(0) dt Ly(0) fy0) = 0) di IP Answer: y(t) =…

A: The solution is given as

Q: t y + 4y + 3√ y(t)dt = 6-7 e²₁ y(0) = 1

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.