3y - t2 dy = 0; y(1) = 1 + y5 dt' 2y4 O t? = y°(3- 2y2) O t3 = y(4- 3y?) O t? = y(7-6y?) O t2 = y²(6 – 5y²)

Q: dy 4. dz at z = - 4 if y = 3x² – 1 and dt Find dt dz dt

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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: [(x²-y²)²] x+y -2 LEK 1J0 du dt

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

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

A: We will find out the required solution

Q: d'y dt? dy - +6y = 21° –t +3 ; y(0)=1, dy -(0) = 2 dt -5 %3| dt

A: At first, we have to find the complete primitive (C.F.) and then we find the particular integral…

Q: Solve differential equation using Laplace transforms. d²y dy + 4 + 4y = 60 y(0) = y' (0)= 0 dt? dt

A: Thanks for the question :)And your upvote will be really appreciable ;)

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

A:

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

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

Q: dx dy + y = x , dt = 3y dt dx dy 1.

A:

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

A:

Q: The order and degree of the differential d³y V dy equation: 7+ is dr3 dx 3,2 7, 3, 3, 1 3,7 Question…

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: y = tan (5t - 21 +1)

A:

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

A:

Q: -+y= cos 21, y(0)= 5 dt y(0) = 5 %3D

A: Thus solution is

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: 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: a) dx dt dy dt =x+√3y+et √3x-y+e³t = ||

A:

Q: *Yx = cos°(t), y = sin (1),z =, dw = 1 dt w =-+2,x= z Z ==, at t = 3 Ans. t=3

A: Given query is to find derivative of w with respect to t.

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

A:

Q: d dt dx dy ruations dt - 2x +2y 1-2t, dyx-0. Giv dt 2 dt

A:

Q: dy + 2 dy + y = sinh 3t – 5 cosh 3t ; y (0) = -2, y (0) = 5 II %3D |3D | dt? dt

A:

Q: Match the differential equation with its direction field. y' = 10 - y \ 20 0:34 // 0.2f Q,1 -Q.31…

A:

Q: What is the solution of given initial value problem? d²x = y + sin t dt2 d²y dx + cost dt dt2 æ(0) =…

A:

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

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

A:

Q: Sketch the direction fields for the differential equation y' = y − x = f (x, y), then sketch the…

A: What is Slope Field: Slope fields, also known as direction fields, are graphical depictions of the…

Q: Solve the system of ordinary differential equations defined by dx/dt+y = cost dy/dt+x = −sint

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Q: dx 2x - y dt dy

A:

Q: dx dt dy dt x + 2y -2x – 3y x(0) = 1 y(0) = 2 | |||

A:

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: dy dy + 7 dt + 10y = e-t dt2

A:

Q: Can i get help step by step please

A: To find dx/dt when y = 2 and dy/dt = 5

Q: Can you help me step by step?

A: The given function is

Q: x +y = x2 29) If - х - у + y2 and dx/dt = 12, then what is dy/dt when x = 1 and y = 0?

A:

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

A:

Q: Please show all work

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Q: By (d) dy 2- = 3t + 2, y(0) = y'(0) = 0. dt By +4 dy + 20y = -3 sin 2t, y(0) = y'(0) = 0. (e) dr² dt…

A:

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…

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.