E f Cx) = x+ X -3x-3:0 Two decimed.

Q: M. y dV, where E- {(x, y. 2) | 0 x* 3, 0 yx, - yEs+y}

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Q: Ans: (x + y)e+y = C y'+--2

A: Given differential equation is homogeneous differential equation which can be solved by converting…

Q: If f(x, y) = xe2y + 6xy, then is dydx given by: e2y + 6 등 2e2y + 6 2 O None of these O 2xe2y + 6…

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Q: For yx + 2x + cx = 9 ,m = 3,Find c at (3,1)

A: Given y2x+2x+cx=9 . m=1. We need to find c at (3,1).

Q: А- If v = t". et. Find the value of n, which satisfies the equation ar (r2 = r2 dv at

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Q: Find the general dafferential equatron (t) t 36y () - o lol00lution of the general solution y Co) =…

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Q: If x"y" = (x+y)** ソ-0 m+n m..n Then, P rove that dx²

A: I use logarithmic differentiation with logarithmic properties

Q: 2.Evaluate . xy+ds where C is the right half of x2 + y? = 16

A: Integrate with use parametric form

Q: Let z=xln(x2+y²-e*)-154xy, x=te, y=est. If the value of Oz when s=2 and t=1 is equal to Ae?+Be, then…

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Q: f(x,y)=xe*/2+275x²y³, then at (1,1) is equal to əx²əy³

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Q: dy If y = V2-x, then find de 10. A 2-x 1 В 2/2-x 1 C 2-x 1 D 1.

A: Given y = 2-x we have to find dydx.

Q: Find the values of the constants a, b, c so that F = (axy + bz*)i+ (3x² – cz)j + (3xz? – y)k Is…

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Q: (c) xy' = y(3– x)

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Q: 5. Show that T = + y? satisfies the equation T + Tyy = T³

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Q: dx -2xcsc 2y – 2x³cos 2y dy sec 2y

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Q: If f(x,y)=xe/2,+37x?y3, then dx²əy³ at (1,1) is equal to

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Q: Find the general solution of using the method of variation of parameters. d²y dy 2- - 42+ 2y = xe 2x…

A: Given,2y"-4y'+2y=xe2xComplementary SolutionAuxiliary Equation is 2m2-4m+2=0⇒m2-2m+1=0⇒m-12=0⇒m= 1 ,…

Q: Let y(x) be the solution for the DE : y = (x + y – 1)2 If y(0) = 1, thenfind y(4)

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Q: » / 13t – 41º + 4 dt = 6. (а) 1 - 5 Jū du: (b) dx = 4x3 (c)

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Q: What is the solution (ry – r) dr + (x²y + y) dy = 0 when 2 and y = 1

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Q: Find the values of the constants a, b, c so that F = (axy + bz3)i+ (3x² – cz)j + (3xz? – y)k Is…

A: A vector F→ is said to be irrational if and only if cure F→ =0 i.e∆ x F→ = 0Given F→ = (axy+bz3) i^…

Q: Show that y %3D Cіx-1 + С2х + Cзlnx + 4x2 is a solution to x3y" + 2х?у" — ху' + у %3D 12х?.

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Q: 1 dz, C:k – 3i] = 3 z² +4z + 13

A: Since we only answer up to 3 sub-parts, we’ll answer the first 3. Please resubmit the question and…

Q: 522 – 7z+3 dz - 12 dt 15w – 13u? + w dw f) e) d)

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Q: Is y = cīt + cf is the solution to y" – 12y = 0? Prove it

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Q: d²y Compute dz? at the point (1, 2) given a² – y² = -3. a) 3 b) 4 9 d) 8 e) O

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Q: Qe/ Salve the Euler- Cauchy equation xy'- xy+9y=o ?

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Q: ..... If F(x.y) = x° + 2x?y - 2y°, then F, = If F(x.y) =x + 2x?y – 2y°, then F, - dy dx

A: We will use various derivative formulas to solve these as shown below

Q: If y = x2 +1 and u= Vx? + 1, then at x = V3 equal to du 1 -4 -1

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Q: Find the solution of the dy Qoec() +y d'ifferential equation.

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Q: Solve the diffgerential Eauation by Separating the Vaciables ex dy 2x %3D

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Q: If f(x, y) = (2x? + 8y²)í, then f_(0, 0) = %3D A) 0 В) 1 C) 4 D) 2 E) Does not exist

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Q: If f(x, y) = (8x2 + 8y³)³, then f_(0,0) %3D %3D A) 0 B) 2 C) 8 D) 1 E) Does not exist

A: Let us consider the two variable function f(x,y) Partial derivative of the function with respect to…

Q: By making the change of variables u = 2, v = x, find the general solution of yfyy +fyx + fy = 1.

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Q: dæ is equivalent to Using the substitution u = x + 1 Vx + 1 1 -du 1/2 du du -1/2 du - 1) /u2

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Q: - show that; L-1[e¬v$] = e %3D 2tynt

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Q: Find the General Solution dy dr = y? – 3y²cos (x) 1.

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

Q: if y=Asinx+Bcosx then prove d2y/dx2+y=0

A: Given,

Q: 4. Solve the following cifferential equation: (- de + 2 xy dy = 0.

A: (4) Given            (x2-y2)dx+2xydy=0

Q: (x, v) = (2ry) i + (r – 2rv) j ,2]. -

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Q: Given f(x, y) = In(3x² + 5y²) then af dx

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Q: If the substitution u= J2x+| iS used, then Só V2x+ī dx is equivalent to ?

A: Substitution will be done by the given variable

Q: if y³ - y = 2x Then, d'y -24y prove that dx (3y -1) |

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Q: If f(x, y) = xe³y + 4xy, then is given by: dydx 3xe3y + 4 3e3y + 4 xe3y + 4 3 e3y + 4 3

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Q: Find the general solution of (x³ + 2y4)y' = 3yx² in implicit form f(x, y) = c. When y(0) = 1, what…

A: We have to solve the differential equation

Q: if y' - y =2x Then, d'y -24y prove that dx (3y –1)

A: Given that: y3-y=2x

Q: Prove that eª (x – 1) = + +c is a solution to xy dx + (y+ 1)e¯ªdy = 0. 2y?

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