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Q: x+y uis = 1 n upi = no • prove that x-+ y-

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Q: Find dz given:Za fixry}==x+2xy+4y2

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Q: dx - x³)². (1 – -

A: Solution: Let Then, singularities  of  f  are  given by…

Q: Q2. Consider the ODE Using u = y ¹, we get A) u' - xu = sin x B) u + 2xu = - 2 sin x C) u + xu = sin…

A: The given differential equation is       y’ - xy = y2sin x    . . . . . . . . . . . . (1)    Now, we…

Q: D2-2D- 3)y = 2sin x; y a. y = C,e™* + Cze* - cosx -sinx %3D COSX b. y = C;e¯* + Cze³* + =cosx – sinx…

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Q: Complete the missing ones: (those highlighted ones) Integrate: [ tan5 3x sec6 3x dx [ tan³ 3x sec 3x…

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Q: 5) Solve y) - 3y4+3y" - 3y" +2y' = 0.

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Q: sechx+cshx b) prove that e2x cshx-sechx

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Q: Find f") if Aa) - (V 1)(x* - 1). %3D O a) -4 O b) 4 c) d) 1

A: Solve the following

Q: the second image is not loading?

A: Here we will use the ratio test for convergence of series

Q: **(sec! I tan /)i + (tan /)j (2 sın cos r)k di tan 7)j 50. sec i tan 7)i 0.

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Q: əz ax+by+sin(ax +by) show that b əx Q5-A) If z = (ax +by)² +e+by+sin( ax a Əz dy

A: The given problem is to show the following condition for the given multivariate function of z.

Q: Stan"(w}sec°(w)ax u )کب + 27 + ه-)J ب)ا 20 - )J No appropriate Match au)کی - 207 - ه-)J du )قی + 27…

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Q: Find V · (V × F), if F(x, y, z) = 6e²*i+ 5xe"j – 2ev³k. %3D -

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Q: Ar)- (xr+1 - })* + (%, – )* + (xr-1 - )* + (y. – )² + (x, – ) + (y+1 - }) + (x, – })* + (y.-1- }) -4…

A: Given that, Lhϕr, s=1△x2ϕr+1,s+ϕr-1, s+ϕr, s+1+ϕr, s-1-4ϕr,…

Q: x+1 dx x(x+3)(x+2)(x-1)

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Q: Solue coscx+y) + (るご+zy+coscx th)), dx

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Q: Compute / tan x · sec a dæ.

A: detailed solution is given below

Q: x²y" + xy' – a²a?y = 0

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Q: 4y" + 36у — csc 3at

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Q: e In (x le) (2- secx dx to be integrable using the formula - se What should be the value of A for u"…

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