olve the following initial value problem using variation of parameters: y" + 4y = cos 3x y(0) = 0, y'(0) = 2 %3D

Q: day dx2 -2 dy x +y = dx +y = 2 cos x

A: We have to find the solution to the given differential equation d2ydx2-2dydx+y=2 cosx, y0=0 and y7=7

Q: Solve: sin(y) dy/dx = e

A: given question is solved using variable separable method of differential equation    final answer is…

Q: Consider dy – y sin(3x) dx = 0, y(0) = 1, x € [0,1] a) solve this problem using RK4 with step sizeh…

A:

Q: cosy dx + (1 + e¯*)siny dy = 0

A: By separating the variables on each side  we can integrate them easily. Given, cosy dx+(1+e-x)siny…

Q: dy Determine the general solution of = 1+ 3y tanx. dx

A:

Q: Solve the given initial-value problem ) = y (y + sin x), y (0) = 1 2xy + cos x %3D 1+y? dx Upload…

A:

Q: Use Euler's method to calculate the first three approximations to the given initial value problem…

A: Given that y'=y-ex-1, y1=2,  dx=0.5 To find first three euler's approximations

Q: Solve the differential equatiorn dy e Cosz =0 by Adams- Moulton method with h=01

A: Step:-1 Adam's Bashforth Predictor Formula is yi+1, p =yi +h24 55 yi' - 59 yi-1' +37 yi-2' +9 yi-3'…

Q: dy +(cos x)y = sin²(x) using first order linear differential equation. dx Solve (sin x) %3D

A:

Q: Find the integrating factor for the following differential equation dy coSx- dx - (sinx)y = x

A:

Q: A particle moves along the x-axis with velocity given by v(t) = 67 sin (at) for time t> 0. If the…

A:

Q: Find the differential dy of the given function. y = 3x − sin2x

A:

Q: dy/dx=x squre root of y for y doesnt equal 0 Solve the differential equation

A:

Q: e (sinh x dx + cosh x dy) = 0

A:

Q: Given that y = sinx is an explicit solution of the firstorder differential equation dy/dx=√(1−y^2).…

A:

Q: 1. еat sin mx dx 0. 8.

A: Given data: The given integral is I=∫0∞eatsin mxdx. The given integral can be written as,…

Q: Compute the following first-order differential equation i. cos x dx +y = sin x , subject to the IVP…

A: Given first order differential equations Using linear differential equation Form

Q: ve the tollowing differential equations: sin*x cos ydx + cos 2xdy%3D0

A: We are authorized to solve only one question, please repost remaining questions Differential…

Q: Solve for the DE: (y²-1)dx + (2xy- Siny) dy =0 When x= -1 ; y= 0

A:

Q: dy Show that given differential equation da y cos z + sin y + y sin a + r cos y +x 0 is Exact and…

A:

Q: The differential equation formed by eliminating arbitrary constants a and b of a sin x + b Y = 9 is…

A: We will differentiate the  y twice to get desired differential equation

Q: ACTÍVITY 2: Differentiate the 1) y = -2 sin 2) s (t) = - WE

A: Apply the differentiation rules for the trigonometric functions to get the derivatives of the given…

Q: (1+x^2)+(y-e^ Arctan x)dx/dy

A:

Q: Use Euler's method to calculate the first three approximations to the given initial value problem…

A: For the solution of the problem follow the next steps.

Q: find differential equation of the following equation 3) dy +xsin(2y) = x cos² (y)

A: Given

Q: IF x = asec'0 and y = atan '0 dy Find at 0 dx 3

A:

Q: H. \ || 20 s s sec (cosx) dy dx siny 3y steb e dx dy >+

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

Q: (dr – ()dy = 0 is exact differential equation. zy?

A:

Q: 2. If y = find the differential dy. Hence, estimate the value of 1 + (1.023 1 +

A: topic- differentials

Q: Find the integrating factor for the following differential equation dy sinx + (cosx)y = x dx

A: We are solving the first question and for the next question post the question againand also mention…

Q: 6) S sech? (2x- 3) dx | ex-e-x 7) S ex+e-x 8) S(eax – e-ax) dx sinh x 9) S dx 1+cosh x 10) ſ csch? x…

A: Given

Q: Consider P(D)y = 0. What conditions on the rootsof the auxiliary equation would guarantee that…

A: Solution: Consider the given Differential Equation P(D)y = 0 Let the Auxiliary Equation of given DE…

Q: 2) / vĩ IneF dx dx etan x dt dx dx 3) 1- sin?x 4) t In vt 5) J Jx (1 + x)

A: Here, we need to find the value of the integration  1) ∫x+35xdx 2) ∫xlnexdx 3) ∫etan(x)1-sin2xdx

Q: Solve the following differential equation given the initial value. dy = tan(x), y(0) =1 dx A y = In|…

A:

Q: The appropriate integrating factor for the following differential equation (3xy – y?)dx + x(x - y)dy…

A:

Q: dy 3-cos?x sin x dx + cos³ (x)y = 1

A: We have to find the solution for differential equation.     According to our guidelines we can solve…

Q: dy + ytanx = y° sec° x dx

A: We have to solve given problem:

Q: A particles velocity is 7 cos(2t) meters per second. at time t=0 its gone  2meters, where is it  at…

A: The velocity of the function is given as:

Q: Solve for the general solition of the followimg differential equation using FOLDE 2. (y - x + xy…

A: Given DE is  (y - x + xy cotx)dx + dy = 0.......(1) We solve this DE.

Q: 1:10 PM Wed Nov 24 Inverse hy perbolio AUTIVITY Oy = sinh (2x+-1) cosh Sza ☺ y= tanhB | -| /2

A: We have to find the derivative

Q: The salution of the differential equation dy subject to the boundary conditions ylo) = 1 and y(0)=0…

A: By using properties of hyperbolic function and trigonometric functions we solve the given problem as…

Q: 1. Given y = 4e* + In x, find the differential dy.

A: See the attachment

Q: If y = In(6 + x8), find the differential dy. Your answer will be in terms of x and dx. Enter dx as…

A: topic - differentials

Q: By using variation of parameters, what is a possible value for u, for the differential equation y' +…

A:

Q: By using the substitution z = cos y, show that the differential equation dy cot y dx X can be reduce…

A: Given differential equation,dydx - cot yx = e3x cosec y

Q: Find the differential equation by eliminating the arbitrary constant/s. e COsX = c(1 – cos y) %3D

A:

Q: 1- Cosh x dy + (y sinh x +e*) dx =0

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.