If W (2t - 1, y(t), 4t -7) = -20, then y (t) = O e +5 none O2-5 O 2 + 3

Q: A solution to y"-4y'+4y xe+ 2x is O A. y = xe* -2x O B. y = xe" O C. y= e* OD. y= xe 2x * None of…

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Q: if z=x+iy then zz= 3- y² +1 3- y² – 1 G- ² |

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Q: If it is known that L {y'' (t)} = -15s+24 with y(0) = -3 and y'(0) = 6, then it can be ensured that:

A: The given problem is to find the Laplace of y(t) from given info, given Laplace of y"(t) =-15s+24…

Q: If z = 3x2 – 2y3, x = 1+ s²t and y = 33 – t2, then dz %3D O a) 6x(1+ s²)+ 12ty O b) 6s²x – 12ty - c)…

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Q: "-y'-12y=x * O y= C1(e^4t) + C2(e^3t) + (t)/12 + 1/144 O y= C1(e^4x) + C2(e^-3x) + (-x)/12 + 1/144…

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Q: 4. Is y = 5e-+7x e-2 a solution to the ODE y"+4y'+ 4y = 0 ?

A: The given solution is  y = 5e-x +7x.e-2x To verify it we will differentiate it

Q: The general solution of (D³+4D)y=0 is Ay=e*(c₁cos2x+c₂sin2x) B y=c₁+c₂cos2x+c3sin2x Ⓒy=c₁еx+c₂e²x +…

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Q: If y(s)=1/(s2-3s+2) , and y(t)=L-1(y(s)) , then y(1)=? (a) e2-e

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Q: 4e3t -2e-2t 5e If A(t) = %3D -5e3t dA find 4e-21 -4e' 7e3t dt -be-2t 5e ? ? ? ? ? ? ? ? ? II

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Q: 2y dr - (x- y) dy = 0, when x= 4, y = 4. O x-y= x O x+y = 4y Ox+4y = x D x- y = 4

A: We will solve it by converting into linear differential equation

Q: 2 3 Compute fyz, if fx, y,2) = x² -x³y² -z'. %3D xyz» OA7 B. 5 OC.0 D. No one correct. O E. 6

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Q: The general solution of the DE y(4) + 16y"' = 0 is O None of these y= C1 + C2x + C3x² + c4e*16x y =…

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Q: -5-S"S, ((m-3)x²+m(m -! x- Yy)-4myx] dydx 2,3m

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Q: 3 If z= then: (2x² + y² )² ' dz az + y- -4z he dz dz + y- 4% az dz + x- y- = 4z az az = -4z

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Q: y + z = 6, x + 2y +3 nsistent, if λ is

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Q: The general solution of xy" - xy' + (24x* – 24 y = 0, is .a - C,xY,(2 /6x) b O C,xJ,(2 6x) +…

A: We have to find the general solution of the differential equation…

Q: 1- S, (xy – y³)dA (1,y]x[0,1]

A: Please ask only one question at a time.

Q: 6. S Se(x² + y³)drdy, wherein B = {(x, y) E R²; 1< x² + y² < 4}

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Q: 10--6A Oa) x- -6 V b) x = 6 c)x- 10 V d) x- -2 Oe) x- -8

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Q: If xy2 3x2y + C, then what is the value of C at (2,2)?

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Q: Suppose that W (y1, Y2) (t) = 4, and y3 Yı – 3y2. What is W (y1, Y3) (t)?

A: Correct option -12 We have to find out the value for Wy1,y3t.

Q: S (x,y.:)= 4x°y° -e°y* ++4y-x" +4y–x'6

A: It is partial derivative

Q: If y" – 2y' + 3y = 0, y(0) = -2, y'(0) = 1, then L{y(t)} = Y(s) = a) 2s+3 82–2s+3 b) 2s+5 g2–2s+3 c)…

A: The given differential equation is y''-2y'+3y=0 ....................(1) Let y=emt ⇒y'=memtand…

Q: (10 – 6y + e-3=) dæ -3.z 2dy = 0 -

A: As per our guidelines, we are supposed to solve only first question. Kindly repost other question as…

Q: If X =V1-t and y= - 3t +t°, what is y' ? O 6(? – 1) /1- O -3 (t? - 1) /1-t %3D 0-6 (t-1)(t + 1) /1-t…

A: x=1-t and y=-3t+t3

Q: z = xy³ – a²y, x = t² + 1, y = t2 – 1

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Q: The general solution of (D³+4D)y=0 is Ay=ex(c₁cos2x+c₂sin2x) B y=c₁+c₂cos2x+c3sin2x Ⓒy=c₁ex+c₂e²x +…

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Q: Find the solution. y' = 5y + e-2x y-2, y(0) = 2 -15x 13e A) y = + 3e 2r1/3 23 139e 15x – 3e -2x \1/3…

A: Given differential equation is in the form of Bernoulli's differential equation.

Q: a) z=-x² + y² c) z² = x² + 2y² e) x² + y²-z² = 1 b) z=-x²-2y² d) -x² - y² + z² = 1

A: match the following quadratic surfaces with the following equations (a) z=-x2+y2

Q: D. 8y = 4x3 - 6x² + 3x + 8e¬*² В. 4у %3D 2х2 — х +3+е-*? Find the particular solution for y' = x3 –…

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Q: (10) Ifr² = x² +y² + z², then Vxr is (а) 1 (b) о (c) 3 (d) None of these.

A: r²=x²+y²+z² Then r=xi+yj+zk

Q: z2+4 Sc 7-szl-4 dz, where C: |z -3i| = 1.3

A: Given integral is  ∫Cz2+4z2-5zi-4dzwhere C: z-3i=1.3

Q: If x2 z2 + y² + xz3 = 3, then dz at the point (1, 1, 1) is: O b. Ос. - 3 d. - 3 Ое. f.

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Q: 5-1. y" - 4y + 4y = t³e²t, y(0) = 0, y'(0) = 0

A: Since  you have posted a multiple  question according to guildlines I will solve first   question…

Q: what is the general solution of y (1 + 3x ) y - v ? Oy = 4 + 3x + Ce %3D = 4 +3z + Ce" 4 + 3x + Ce…

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Q: The general solution of the DE: y" – 3y = 0 is Select one: y = ce² + cze³z y = c +cze³z y = ce² +…

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Q: What is the particular solution of (3r + 2y?) da + (4ry + 6y2) dy = 0 when r = 2 and y = 0 ? O7+…

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Q: The general solution of the DE y" - 2y' - 3y = 0 is y = cqe*+ c2e-2x O None of these y= Cqe*+ c,e3x…

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Q: - y If z=x²sinh then дхду 4 O A. (-x3– 3x?y + 2xy2 – 32x) / 16+x² – 2xy + y² (16+x²- 2xy + y²) ² O…

A: This question can be solved using the concept of derivative of hyperbolic function.

Q: The general solution of æy" + xy' +(3x² – 16)y = 0 for a > 0 is Y = OCiJ/5 (4x) + c2J_va(4x) None of…

A: The Bessel's equation of order ρ is given by  x2y''+xy'+x2-ρ2y=0  Then the general solution of the…

Q: dy dx + 3x²y = 6x²

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Q: 17 c. Find the general solution of the D.E. 2 y" +4y'-8y = 8×-4e²* +4

A: We solve given DE by using method of undetermined coefficient.

Q: note that X - y +z = e2 and 4x – 3y + 2z = e2

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Q: v - 2w + x + 2y - z = 6v +3w- 2x + 4y - 3z -v + 2w – 3x + 4y – 5z = Ev + 13w – 2x + 8y – z = -

A: Gauss Jordan Method: Gauss-Jordan Elimination is a method for finding the inverse of any invertible…

Q: The general solution for the DE v32e2x, is given by O a y= Ce*+ C2e*+ 1 Ody Ce+C2xe* + e O e. None…

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Q: 4y" + 16y' + 17y 0 y = 1, t 0 and y = 0,t = n

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Q: If xy + 2xy = 8 then at the point (1, 2), y' is Select one: O a. а. b. O c.-1 O d. О е.0

A: Find the differentiate with respect to x at the point (1,2)

Q: 2 The general solution of y +xy+ 9x* - 4 y = 0 is: O a C,J,(3x) + C, Y,(3x) Ob. C,xJ,(3x) +…

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Q: /25-22-y2 zVx² + y? + z² dz dy dr

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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.