let lly):xy"-x (42) y' + (x42)y a. Consider the homogenzous dipperential equation Lcy) = i the t y=X on (O, o) show jolu tiom of solun * do solve Lly)=xeX Liy)=xY eX

Q: f= x? + क) | + ला (i) of =? (üi, af मु] liv) of

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Q: If a and b are integers, then a/b is always a rational number. True False

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Q: FCx): 2x-5xナ3 find f'co).

A: We are solving the first question and for the next question post the question again and also mention…

Q: 11. Integrate the function. y? -dy (49 – y² ) 5 y 7y +C - sin"' y + C V49 – y V49 – y² V49 - y -…

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Q: The equations ry? + 5zzcos(u) + ye" = 10 and zyz + ze" - 4u = 12 are solved for u and v as functions…

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Q: W = spanR{1, cos² (x), sin² (x)} = R + Rcos² (x) + Rsin²(x) Justify for each of the subsets {1, cos²…

A: Given: W=spanℝ1, cos2x, sin2x=ℝ+ℝ cos2x+ℝ sin2xWe need to justify for each given subsets that it is…

Q: 2. Determine whether the functions f1(x) = e2", f2(x) = e=2#, and f3(x) = sinh 2x are linearly…

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Q: 3) у %3D 2u* + 1 x = 5u? – 5u -

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Q: along the following paths C:(a) x=2t^2, y=t, z=t^3 from t=0 to t=1; (b) the straight lines that A ·…

A: We will use parameterization to find line integral

Q: What is the value of t in terms r, s, and u In the equation

A: The solution is easy to see

Q: f(i) = 5, f'(i) = -3i, g(i) = 3i, and g'(i) = 4. Find (fg)'(i).

A: Given fi=5,f'i=-3i,gi=3i,g'i=4. Find fg'i.

Q: Find G′(w) if G(w)=5/ 9w^5 +7 sqaure root w. G'(w)

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Q: Verify that fy = fx ху ух f (x, y) = 2x'y' -x'y b. f(x,y)=(x' + y²)° а.

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Q: 1. If f(x, y)=3x' cos y– y sin x– 2.x In y- yln x-4x²y, find ôf ôf d²ƒ _ô²ƒ

A: According to question given thatf(x,y)=3x3 cosy-y2 sinx-2x ln(y)-y ln(x)-4x2y

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A: Here we have to go option wise and choose the option with; y(0) = y'(0) = 0. Clearly we can see…

Q: (4) M" - afg' -4fg= 0; Y@-1, g'()=0

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Q: a) z=cos² (3 xy) onde x=p+eº ey=p²-2e³8 b) z=4x³y onde x=3p²+0² e y=p²-40²

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Q: ind the fangent line for... 1x1) = +²+et ( (1) = sh (k) + t at t=0 B) r(e) = sinG + case at 6: T

A: Explaination of the answer is as follows

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Q: Pron a. If u = f(x, y), where r = e' cost, and y = e' sint, show that (3)³ + (3) ² - - ² [(-)* +…

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Q: Sketch the direction field of the DE y'=2x+y.  (Plot 9 or more points) Then sketch approximate…

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Q: 1) FIND F'): C P)= (x D(2x+)

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Q: Find дх (дхду) 6,e at the point(7,), where g(x,y) = cos(y) [sen(x) + xy].

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Q: x'+y° Q4. If u = sin- sin-'( -), Show that x+y ди X- ди + y- = 2tanx (2 + ду

A: If u=sin-1x3+y3x+y, then show that x∂u∂x+y∂u∂y=2tanx.

Q: a3 f 2- Find the third derivative for for f (x, y) = sin əx3 -2sin?cos()+2 sin) sin By'sini )+2…

A: The given function isf(x, y)=sinxy

Q: Q2// B :- If u+v3e"cos y and u- v=e' sin y find the Jacobain of the function alu,v at dx.yl (x.y)…

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Q: Suppose that I'm (f`∞x) = (x (24-1) and f(0) = 3-2i, f(1) = 6 -21, Find f(1+i)

A: Given that Imf'z=6x2y-1 To find: f(1+i).

Q: 1 g(u) = V5и + 8 then g' (u) =

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Q: Find dxdz -2 -3lnax) a= constant

A: find d2ydxdz y=(z14-3lnax2)-2

Q: Calculate zu for z = 2x-y 1, x = e²u cos(3v), y = e²usin(3v) x+3y'

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Q: 5. What are the coordinates of the JNBS if J'(-2, 4), N'(3, 5), B'(2, 3), and S'(0, 2) after R(90".…

A: Given: J'(-2,4) , N'(3,5), B'(2,3) and S'(0,2)

Q: x2 + 8x +3 10) y=- _ dy A) 3x2 + 8x - 3 dx X Find the derivative. A) 11) s= t3 tan t-√√t ds dt C) dy…

A: