29, + 16y=0 geoJ = 2, go)= -2 2. 31, dy dy -54 =0 dt

Q: ye(2y*) dy

A: Given the integral I=∫ye2y2dy     ....(1)

Q: 5- dy/dt = y²(y+1)(y-3), -∞<Yo<∞

A:

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

A:

Q: 18y sin3 9y2. 10) +3 cos V9y2 + 3 dy + 3 cos

A: See the attachment

Q: Can you help me step by step?

A: Differentiate both sides w.r.t. t. Apply product rule on the right side. Product rule: (uv)'=u'v+uv'

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: Calculate 2 4-y2 IL dy de y dx dy. T sinx SSasing dy dx @ $ ydydk

A: Hello, thanks for your question but according to our policy I am answering the first three subparts.…

Q: dy dt t2

A:

Q: Find the location and velocity at t = 4 of a particle whose path satisfies dt dr (3t-1/2, 5, 8t) and…

A:

Q: find particular solution of (16x+5y)dx+(3x+y)dy=0. If the curve to pass thru the point (1,-3)

A: Given: 16x+5ydx=-3x+ydydydx=-16x+5y3x+y               It is a homogenous differential equation.…

Q: : )-+(÷), zw= (C) dx 1 et %3D dt 1 (: :)-+(-), -= (C) dx dt 1

A: Given dxdt=0110 x +ete-t Here let take A= 0110A-λI=-λ11-λ=0λ2-1=0λ=±1 Hence the eigen vector for 1…

Q: 3. Linear DE of Order one 2y(у? — х)dy %3D dx

A: Linear equation of dx/dy form is made

Q: EXERCISE 1 dy -dx = 0

A:

Q: 2. у(у+ 2х — 2)dx — 2(х + y)dy 3D 0

A: A differential equation of the form M(x,y)dx+N(x,y)dy=0 is said to be exact iff, ∂M∂y=∂N∂x

Q: dy If y = 2sin 3t then aY is: dt

A: we know that, derivative of a^x = lna * a^x  so from this we will solve the quesiton

Q: dy 4 – 5y = e-3t sin(4t) ; y (0) = 3, y (0) = 10 dy %3D - dt?

A: We solve the given IVP  y"-4y'-5y=e-3tsin(4t)........(1) y(0)=3, y'(0)=10.......(2)

Q: dz %3D dt

A: Given that: z3=x3+y2, dxdt=2, dydt=1 and z&gt;0.

Q: Show that (i) | te 3 sint dt 50 -3t %3D

A:

Q: [-+] 5t dy 3.1는-51%3D-y dt

A: This is a linear 1st order differential equation.

Q: Assume that y = 5x and dx/dt = 2. Find dy/dt.

A: Consider y = 5xApplying derivative with respect to t on both sides and plugging the values:

Q: arcsin 4y dy 1 – 16y2

A: Given: ∫arcsin4y1-16y2dy

Q: Solve (1+siny)dylx=[(2ycosy-(secy+tany)]dy.

A: This question is taken from a differential equation in which we have to solve the equation and take…

Q: A. = 2x - y + sin2t dt = 4x + 2y + 2cos2t (variation parameter). dt

A:

Q: I = f, (sinhz + 1)dz. %3D

A:

Q: 2T sin (2) dydx 0,

A: To evaluate the double integral, ∫π2π∫0x3sinyxdydx.…

Q: Intergrate:

A: To evaluate the integral.

Q: Find at x = 4 if y = 4x² - 2 and dt da dt Question Help: Video Submit Question dt = - 3.

A: We are asked to find the derivatives.

Q: Write the general solution to y= arcsin 1. Oy=+2 tk Oy=tk Oy= T ak

A: Given :y=ascsin(1)

Q: A volleyball is moving 16 m/s at 25o North of straight down. If +x is East, +y is North, and +z is…

A: Draw the sketch, as follows: Since the ball is moving 25° North of "Straight Down" direction, its…

Q: dy If y = (t + 5t + 6) (2t² + 4), find dt dy %3D dt Submit Question

A:

Q: Integrate both sides dy = -dx

A: the given integral equation is                             ∫1y2dy=∫1xdx

Q: #2. Show that the line integral (sin y dx + (x cos y – sin y) dy)

A:

Q: х2 9 dy + sinx - у %3D0 dx

A:

Q: Solve = 1 +y, y(0) = 0 by Picard's method. %3D dx

A:

Q: dy 40. dx = VT/2 2ху 3D 1, у(0) 3D

A:

Q: 1. d²y dy +6- dt² dt +8y=-4 cos(3t)

A: We need to solve D.E. As per Bartleby's guidelines we can solve one question from multiple question.…

Q: 12) / Зy sin(5y?) dy

A: Solution:

Q: tan y dy 1-tan2,

A:

Q: d's 元 =-4 sin 2t-- 2 s'(0) = 100,s(0) = 0 %3D dt?

A:

Q: Explain, the given differential 3x²dx + 2yz dy + y² dz is exact or not.

A: We will check whether  3x^2dx+2yzdy+y^2dz is exact or not.

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

A:

Q: dy 38. dt у сost

A: Given Information: The differential equation is dydt=ycost. Calculation: Calculate the general…

Q: Find dy/dx: 1. у%3D Jo = San* sec? t dt

A: A detailed solution is given below

Q: 1) S 2 sec y (tany – sec y) dy

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

Q: dy/dt=0.3(y-200)

A: Separate the variables and integrate both sides.

Q: Solve for the general solution of the given non-exact DE. y(y + 2x – 2)dx – 2(x + y)dy = 0 - -

A:

Q: dy -2y 3cos3t – 11sin3t dt? dt

A:

Q: dy dx 2 at x = 5 if y = 4x? + 5 and dt = 4. Find %3D dt

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.