•2X Solve the DE (D-1)4= 3 sinx+ 22 - 2x 2 (D-1)y=

Q: 3. f(t) = 2e3t sin 2t – 3e3t cos 2t -

A:

Q: 8. (D2 – 10D + 34)y = -cos3x

A: Answer and explanation is given below

Q: dx dt -1 -3 [:] 2 with x(0) 4 Give your solution in real form.

A:

Q: cos (2t + ) dt = e2t-3 4-

A:

Q: Find the general solution of the equation d2y/dx2 - 2dy/dx +4y =2ex sin2(x/2)

A: Given the given differential equation is d2ydx2-2dydx+4y=2exsin2x2

Q: Solve: Tanxdy+ y°Sin²xdx=0, y(0)=1 а. у"(3-Сos2x)-2 b. у(-2х + Сos2х) -1 d. y(-1+ Cos2x) — х с. у?…

A: This question is related to differential equations, We will solve it using given information.

Q: y''-5y=sinx

A:

Q: Solve the equation: (D² - 1) y = 0 Oy=c₁e* + c₂xe* + c3 cos x + c4 sinx Oy=c₁e¹* + c₂e + c3 cos x +…

A: A detailed solution is given below.

Q: D2 - 3D – 4)Y = sin 2x

A:

Q: Use Method of Undetermined Coefficients: y" - 2y' + 5y = 4e*cos2x +x2 2

A: We have given a differential equation ,  y'' - 2y' + 5y = 4ex cos2x + 52x2 First we will find…

Q: COs 2.r dx x² + 2x + 2

A: In this question, we find the principal value of the integral by using residue theorem

Q: e" sin°(2x) (d) y = In 2x2 + 1

A:

Q: b. y= 2 sin 2x+1

A:

Q: Solve y" – 4y' + 8y = e2" + sin 2x 3.

A:

Q: 2. (D2 - 4D + 3)y = e3x cos 2x

A: Recall: Roots of Auxiliary Equations : If All roots,m1,m2,...,mn are real and distinct then…

Q: Solve the equation sin u = -1, for 0 … u 6 2p.

A: Given, the equation sin u = -1, we have to solve this equation in [0, 2pi).

Q: Q(3) Solve (D3 + D²)y = 3x2 + 6 sin x – 2 cos x

A: As per our guideline,we are supposed to answer only one question.Kindly repost the other question.…

Q: 4. (D² – 10D + 34)y = -cos3x

A: Using method of Linear Differential Equations with constant coefficients.

Q: using undetermined coefficients (D^2-2D+2)y=24e^x sin3x

A: Given: (D2  -2D+2)y=24ex sin3x

Q: Q.No.3: a) Solve Cauchy-Euler equation d'y 3x3 dx3 d²y dx2 dy + 9x? + 6х— — бу %3 1+x3 dx

A:

Q: Solve: y" - 6y + 15y = 2 sin 2t, y(0) = -1, y'(0) = -4

A: Let's solve given diffrential equation.

Q: 4x + Vx Y = (a) 7x2 – 3 et (b) y = 7x³ cos x 19

A:

Q: d²y Solve: dx2 dy + 42+ 4y = 4x²e¬2x, cos 2x %3D dx

A:

Q: Solve (D2+1)y = sin x sin 2x %3D

A:

Q: L sinh-t %3D .a 3s2-4 6. .b O 9s2 -4 .c O s2-4 3. .d O 2s2-4

A: We know that  L( sinh(a)t) = (a)/(s^2 - a^2)

Q: Find the solution. (D2-4D +7)y = 0 y = e-2(c,cos3x +c,sin3«) Oy= e"(c,cos/Zx+c,sin/2x) O y-…

A: Given differential equation is (D2-4D+7)y = 0

Q: Q7// find the general solution (sin-1x + 1 y)dx + sec-1xdy = 0 1 xVx² – |

A: The detailed solution is as follows below:

Q: Find the general solution: 2y" + 3y' +y = 2e2 + x² + 3 sin(x).

A:

Q: d²y + y = 4 cos x dx² Please solve this equation by hypothesis (V)

A:

Q: Q/ Solve the differential equeion tx²y)dy=2xydx

A: The Given differential equation is: (x2-y2)dy = 2xy dx Rearranging the differential equation:…

Q: (D5+3D + 4D³ + 32 cos (2a) + 3e 12D²) y = 16 sin (2x)

A: The given differential equation is…

Q: Find the general solution of y" – 4y' + 5y = sin (x)

A: The given differential equation is  y" - 4y' + 5y = e2xsinx

Q: che general solution of -V - 6y = 6x3 + 26 sin 2x

A:

Q: d²y 9. +y= sin 3x cos 2x 2

A:

Q: Q16 a) / 31 3t+2 b) dr cos² a √5+tanz » /; c) [₁² dt (3-5t)²

A: Given :(a) ∫3t3t+2dt(b) ∫dxcos2x5+tanx(c) ∫12dt3-5t2

Q: 13. (D² -1)y = x³ sin 3x

A:

Q: Solve the nonhomogeneous equation using the method of undetermined coefficients: y +4y=x-2 cos 2x,…

A: The solution is given as

Q: Solve (D2+9)y=cos 3x+sin2x

A:

Q: d?x + 4x = sin2t Q5: Solve: %3D dt2 Using variation of parameters method?

A: Answer

Q: The general solution of (D2-2D+ 1)y=2sin x A у-сје*+ с2хе* + sinx + cos х y=cqe*+c2xe* +2sinx В ©…

A: Note -  Acc. to Bartleby guidelines we are supposed to do only one question. If you want more to be…

Q: Solve the equation [cos (2y) - (3x^2)(y^2)]dx +[cos (2y) - 2x sin 2y - (2x^3)(y)]dy = 0

A: To solve the given differential equation. First we check whether the differential equation is exact…

Q: 3x*y+2x +y² +5 = cos(2x)+5x

A:

Q: SOLVE USING THE METHOD OF VARIATION OF PARAMETERS d³y , dy 1 V1- cos²(x) dx3 dx .2 II

A: This given equation is third order non homogeneous ordinary Differential  Equation to solve this we…

Q: Find the general solution of the equation y" − 4y' + 3y = sin(x)e²x -

A:

Q: 6. Find the general solution of (D²+D)y=sinx.

A:

Q: Solve : = - 3 y t16y =0 fus uwer. = 3 cos 4x- Sin

A:

Q: (D3- D2)y = cos2t a. y, = -cos2t +sin2t 10 20 b. y, = - cos2t -sin2t 10 20 c. p =cos2t- sin2t 10 20…

A:

Q: Find the general solution y" +4y'+5y=2e +cos.x -2x

A:

Q: (D3 + 2D2 – 16)y = 40e2x + 80 sin(2x) %3D

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.