Verify that the conclusion of Clairaut's theorem holds, that is, u, Uxy = "yx' u = x'y8 – y? With u = x'y8 - y', we have the following. ,7,8 Ux = Uxy Uy Uyx %3D Since u, = uvx Clairaut's theorem holds for u = x7y8 – y7. ху II II II

Q: Calculate û x ô if û = ĵ + 2k and û = -i - ĵ + k. %3D

A: Topic = Vector   if u→ =a1i+a2j+a3k and v→ =b1i+b2j+b3kthenu→×v→=ijka1a2a3b1b2b3

Q: Solve the differential equation by variation of parameters. 1 2 + ex y" + 3y + 2y =

A: The given differential equation is y''+3y'+2y=12+ex. The objective is to solve the differential…

Q: y®y' – 8y9 = ex ,8,

A: On simplification, we get

Q: Transform the equation: 2x2y'' + xy' + 3y = 0 to the form of: a(d2y/dz2) + b(dy/dz) + cy = 0 (a,…

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Q: Show that x +2 and oe) = *+6

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Q: Determine Cif u=v=0 (20 — 5и + 3)dv — (20 + 4и — 6)du %3D 0

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Q: The equations ry? + 5xzcos(u) + ye" = 10 and x³yz + xe" – 10u2v² = 30 are solved for u and v as…

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Q: d. (6j-7) / (3j-12) е. (8e/4)(Зе/8) f. (2230)/ (4260) 12ejs g. 34 h. (2ei*)(2/4) i. (5(cos(20) +…

A: According to our guidelines we can answer only one question and rest can be reposted.

Q: If X = U+v , y =U-V then Show that + 2 du? = 2) ( %3D nene Than ded uce that wok cu+ v*+ (u+v) g…

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Q: Q3. Find y= fx) such that y

A:

Q: 2 a) y = Find y'. 3e (ax-5)4

A: Explanation and solutions is given below.....

Q: dw и and if w = x³ + In (²) dv E) + y, x = u² –" + 5 and Find - ди y = 3v + 5u and point…

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Q: 4) Find the adjoint of the operator Lu = u" + 4u'- 3u, where u'(0) = -4u(0), u(1) = -4u(1).

A: The objective is to find the adjoint of the operator, Lu=u''+4u'-3u where u'(0)=-4u(0), u'(1)=-4u(1)…

Q: Fnd llull, lv , Uov, and d (4,v). (-1,7) , v- (1,9)

A: According to our company guidelines we are supposed to answer only first 3 sub parts. So here I'm…

Q: If Fu,y, z) = xzi + xyzj =ý k, find v.È %3D ........

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Q: Eliminate the arbitrary constants A and B in the equation y = Acos5x + Bsin5x. O A.y" - 25y = 0 O…

A: Solution :  Options (B) is correct

Q: The roots of the characteristic equation of y"-7y=0 are:  a. √7.-√7  b. 0, 7 c. 7,7 d. 7.-7

A: Here I am attaching image so that you understand each and every step.

Q: Differentiate w.r.to "x" y = xsin-1x +x/(1-x3)

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Q: The antiderivative of the function sin (Gx+7) is:

A: Given : sin12x+7

Q: for 3x'z -x'y² +2z + 3xy = 0 ( Hint: Let %3D F(x,y,z) = 3x z - x'y? + 2z +3xy) %3D

A: Explanation of the answer is as follows

Q: Verify that the conclusion of Clairaut's theorem holds, that is, Uxy = Uyx" u = x5y8 - y5 With u =…

A:

Q: Find those constants a, b, c, d such that f(z) = ax² + bxy + y² + i(x² + cxy + dy?)

A: The given function is : fz=ax2+bxy+y2+i(x2+cxy+dy2)

Q: Series Solution Method. In each of Problems 1 through 20, solve the given differential equation by…

A: Given y''+5y'+6y=0,   x0=0   To Solve: The differential equation by means of a power series about…