4x = 0 %3D 4y + i = 0 x + y 8 = 0 (х, у, 1) %3

Q: S-8r-7)dv a. 3. dt 1-16r b.

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Q: у" — бу' + 9у %3 t'e", y(0) 3D 2, У (0) 3D 17

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Q: 3. y' +y y2 A. y 1+ Cex = e-3x + C B. y = e-3x +C C. y 1+ Ce-3x D. y = e3x + C %3D

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Q: 1. y' – 5y = e5x ;y(0) = 0 2. y" + 4y = 0;y(0) = 2, y'(0) = 2 %3D %3D

A: In the given question we have to solve the given differential equations by using the Laplace…

Q: (tVE2 + y² – y)dt + (y/E² + y² – t)dy = 0o %3D |

A: We will find out the required solution.

Q: K = 3. L = -2 jSgĀ = (3, -2) .B= (4 , 3) jS 131 (4) KA +LB dg %3D %3D (1) A +B (2) KÀ (3) LB

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Q: 3x2 +- 8(y + 1) = 0 dy y+1 C 3(: 100 - designed by freepik 24C X=Yi+(x20)

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Q: y- 2x = 3y - 2 %3D Oz= 3yIny +1+Cy Oz= 3lny +1+ Cy Oz = 3y Iny +1+C Oz= 3y Iny + Cy

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Q: 6. J-3 0 + 4y +4) dy 1. 8. (3w2 - w- 1) dw 9. 10. 31-3 dt

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Q: (c) S, y*/1- y² dy

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Q: The general solution of : y' = y In(y) %3D Select one: а. y = c ex b. V = e ex+c C. V = ex+c d. y =…

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Q: 4. use "Homogeneous Equations" method (y2 + xy)dx +x²dy 0 %3D

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Q: (D2 — 4D + 4)у — еЗx A. y = cqe2* + cze2x + e3x B. y = ce2* + c2xe2x + e3x C. y = ce2x + cze2* +e 1…

A: to find out the general solution of the given differential equation

Q: (3x"-1)(3) %3D 3 Y +1 e 3x"-1 s 3x"+xY =4 %3D -) m =4 30 that 3x +1 %3D 3x4+1

A: See the attachment

Q: Solve Xy"-xy' +y = a+3ln(x), y)=Q , yl)=1 %3D

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Q: (D^3 - 2D^2 + D) y= xe^x + 1, y(0) = y'(0) = 0, y''(0) = 1. By inspection method.

A: We are given a third order non-homogeneous linear ordinary differential equation as : y''' - 2y'' +…

Q: Find the solution. xy'+ xy = 1 - y, y(1) = 0 A y = x-(1 – e!-*) B x = y-(1 + e!-x) 2y = x³(1 + e!-2)…

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Q: Obtain the general solution. (xy + x) dx = 2 2 y + x + y¯ +

A: The given differential equation is…

Q: 1. x = BC %3D X + 3 • A C 2x %3. ML = •P 5y Зy +4

A: here we have to find the value of x and y in both question. the solution is following.

Q: Find the solution for: y' – x e = 0 using separation of variables.

A: Solution of differential equation

Q: 3 9 dx dt -1 -3 2 and x(0) 4 ||

A: In the question it is provided a system of differential equations:

Q: +2x (D³ – 4D’D'+ 5DD" - 2D") z=e** + Vy +x.

A: Given PDE is D3-4D2D'+5DD'2-2D'3z=ey+2x+y+x We can write it as D-D'2D-2D'z=ey+2x+y+x             (1)…

Q: 8.s Y°+y² _ dy + y² – 1 y2 + 1 8. S

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Q: y" + 3 y" + 2 y = (x+ 1)e²". %3D

A: We have to find general solution of given differential equation.

Q: 5. y" – 3y' +2y=0; y1 =e*, y2 = e2x; y(0) =1, y'(0) =0 %3D -

A: Here is the solution:

Q: Integrate зав тв2 xp (2x +B) da t 2 y 9 x ₂²¹ + xop dp x. P (2x +B) Jyo xo, Yo, y tIR. Choose to, yo…

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Q: y" – 4y = e*, y(0) = 0, /(0) = 0. %3D %3D

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Q: d³x d2x dx -2- =0 dt dr3 dr?

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Q: (2āx – 2āy – 2āz). (x1 + 1)āx + (y1 – 3)āy + z,āz = v12 * d %3D 2x, - 2y, - 2z, + 8 = v12 * d → -3 +…

A: Explanation of the given expression. 2a¯x-2a¯y-2a¯z·x1+1a¯x+y1-3a¯y+z1a¯z=12*d

Q: 14. t- 3 x+2 x +1 %3D 15. x +1 1 %3D 3 2 y2 +4 y+ 2 y-2 y2 - 4 16. y 2 17. d +4 %3D d² + 3d – 4' d-…

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Q: y"' + 2y" + y' = e*, y(0) = 0, y'(0) = 1, y"(0) = -1

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Q: V3/2 6. dt VI - 12 1/2 1 + Vx dx 64

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Q: 1) y" + 4y = 4 sec (2x) 2) y" + y = csc(x)

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Q: // (x+ y) dA, A = {(x; y) E R² : x € [0, 1), y E [2x, 2V]}; A

A: To evaluate the given double integral

Q: 1) y"- 3y"+3y'- y = ť°e' ; y(0) = 1, y '(0) = 2

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Q: 1l y" + 4y' + 4y = e-2x %3D x2

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Q: D.Linear Homogeneous DE with Constant Coefficients: 2. (D2 – 2D – 3)y = 0 ; x = 0; y = 0; y' = -4

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Q: Find the solution. xy'+ xy = 1 - y, y(1) = 0 y = x-2(1 + el+*) Bx = y-(1 + e'-") y = x-(1 - e'-) D…

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Q: YH = 2x Y HW= 3x – 12 %3D Find YH H W

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Q: 1.y' + 6t = e*t, y(0) = 2 2.y" + 6y' + 4y = 0, y(0) = 1, y' (0) = 0 3.y' +t = e5t, y(0) = 1

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Q: y =-x² +2x+7 y =-2x +2 → Solution(s): %3D S y = x + 2x –3 %3D y= 2x+1 %3D → Solution(s):

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Q: y' + 2y = 1 + e−x, y(0) = −4

A: This is the first-order differential equation; it is in the form of Therefore, Then find…

Q: 11. y" – 2y' + y = e', y(0) = -2, y'(0) = 2, yp(1) = Įře' %3D

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Q: Y+ 2 - 3W -2 %3D 3x +y -z + sw - 0 2x + y - z t 4w : o * + y -2 + 3w :0

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Q: (iv) SSS 2x dV, D:0 < x < /4 – y²,0 < y< 2,0 < z < y.

A: Answer

Q: (ii) y" – 4y' + 4y = e3", y(0) = 0, y'(0) = 0. %3D

A: We have to find general solution of the given initial value problem.

Q: 3x d.A, A= {(x; y) E R² : y E [0, 1], x € [y, e®]} .

A: Given: A double integral ∬A3xdA, A=x;y∈R2:y∈0,1, x∈y,ey ∬A3xdA=∫01∫yey3x dxdy=3∫01x22…

Q: Vy. (ii) SS x²y dA , E:x = y² and x =

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Q: e 3z -で dz (ez + e5z)2 I = 0,

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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.