Q1 Consider the DE (1 – t)y(³) + 3x²y' — y = sin x. - (i) Order of this DE is_ (ii) Degree_ (iii) Is this DE linear or non linear? Ans.

Q: A- L [ Sin2t + cos2+] ² 2 B 32 3-2 [37-² + cost's *] 3 2

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Q: 31²+1 dt = Compute:

A: Dear student as per our rule in one session we can only solve one question. Please post the other…

Q: 4. Perform the indicated multiplication of the two differential operators: (D –x)(x²D– 2x).

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Q: 3i +2V2 - 5n -4i +6(1 +a T/4 [(3sec2 t)i - (5 + sin t)j - (6sec t tan t)k)]dt Find 0. 2 2-57T-4 3i +…

A: ∫sex2xdx =tanx+c∫(constant)dx=x+c∫sint dt =-cost +c∫sect tant dt =sect+c tanπ4=1cosπ4=12secπ4=2

Q: дz az Use the chain rule to find and Əs Ət əz Əs əz at = = ¹(=), z = tan u = 3s + 5t, v = 5s - 3t

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Q: 7. Set f(x) (a) (b) (c) (d) = 2 +4 8 cos 2x, 2sin2, + e-8/2 s² + 4 S s² +4 8 8² +4 (e) None of the…

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Q: Find of z = In(xy)

A: Given,Z=ln(xy)differentiating both the sides partially w.r.t. x∂z∂x=1xyy1∂z∂x=1xagain differntiating…

Q: 1] Evaluate (a) -S (s²+1) ² {t sin (b) S 1/2 5² (s² +¹)² (d) S

A: Find Laplace of tsin(t/2)

Q: *) Use the Wronskian to determine whether the functions y₁ = sin(3x) and y₂ = cos(4x) cos(4x) are…

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Q: lim tanx i. x→ 0 lim In(1+ x)] 11. x→ 0 lim sin ax i1. where a and b are constants. r0sinbxr

A: We are only allow to to do first question and three subpart of question So if you need rest of…

Q: Consider the DE y"+exy'+ (sinx) y = ex+2lny then the order of the DE is ✓ and it is

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Q: What is the B of f(x, y) = tan (x3³+ 2xy)? [sec ² (x²y³+ 2xy] (3x²y² +2x) [sec² (x²y³ + 2xy ] (+²+*+…

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Q: O [-5, -1) U (1,6] O (-5,6] O [-5, 6] O (-5, -1] U [1, 6] Find the domain of r(t) = (ln(t + 5),…

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Q: Stan"( 1 -tan m+2 -tan m+1 m+1 1 m+3 Evaluate A B Ⓒ D tan" (x) sec¹x dx. (m + -2)(x) + ¹) (x) - 1)…

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Q: 2- Find the third derivative for əx3 for f(x,y) = sin) )+2 sin) sin)+3cos°) 8y3sinz s()+2sin()…

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Q: se-2s -)=D 's²+45+3

A: Given,

Q: Evaluate I= √ (sinx+2y) dx + (6x+y)dy for the non closed path ABCD in the figure.

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Q: Simplify (if necessary) then 2 Compute: y" +Éy' for a2 y(z) = rar (zx+ cosx')] [6(cosh2x- sinh2x)] d…

A: given yz=∂2∂x∂zz2x+cosx96cosh2x-6sinh2x36cos2πxddx3x2 claim- if necessary simplify then compute the…

Q: of of +y y Let f(x, y) = x$y² tan Then x equals X

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Q: Discuss the continuity of the function 2ху +y? f(x.y): (x, y) # (0,0)

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Q: Y 4 1.2) ["se sec ¹ √e de e 20) ff 2² 1 x² ln x dx

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Q: Q.13.a) s dx x2+2x+1 b) Sx sinvx dx dx c) J Tx+V% 1E / E

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Q: None

A: Given, a)   f(x)=(x-2)2  b)   f(x)=(x-1)(x+1)

Q: Write the system x'= e"x – 4ty+9 sin(t), y' = 7 tan(t)y + 9x – 4 cos(t) in the form = P(t) + F(t).…

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Q: If v(r, y) is a harmonic conjugate of a harmonic function u(x, y) show that the function g(r, y) =…

A: Harmonic function: A two variable function ux, y is said to be harmonic, if the function is twice…

Q: Let u (z, y) = 8r + 3ay- y Part (a) Show that u is a harmonic function. Part (b) Find a harmonic…

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Q: (b) (sin 0)y"+ (0+ cos 0)y" 2tan@

A: Given: sin θy'''+θ+cos θy''=2 tan θ (a) The number of the highest derivative in a differential…

Q: Evaluate tan" (x) sec4x dx. 1 1 A -tan 2) (x). + (m+2 -tan" (x) + C m+2 m (m+1) ¹) (x) (m- m+1 1…

A: Evaluate: I=∫tanmxsec4xdx

Q: find the derivatives complex funcation. {tanh¬'(iz +2)}-1,

A: fz=tanh-1iz+2-1=1tanh-1iz+2 It is known that tanh-1x=11-x2 so it follows:…

Q: V Sove using variaton of parameters recuction of order or (D² - 2D+1) y = e*(e*+)*

A: Please find attachment for the details solution

Q: 2x³y' = y(2x² - y²)

A: We have to solve the given ordinary differential equation.

Q: het f be a bounded real-valued funtim on TR" Define (Mst)(a) = Aup {tla): Ix-al <8$ %3D (mg t)(a) -…

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Q: Qi Write the order and degree of the given. ODE'S.check either these equations aye nón-linear. Also…

A: Consider the given function. y''+x2y-2y'=sinx As the maximum order of the derivative is 2.  So, the…

Q: Find the residue of - (:- 1)* at its pole

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Q: Compute sin (3r)dr (25z4+1)2 -

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Q: 1. Evaluate f{(t² e2t + sinh2t)}

A: As per our guideline we are supposed to answer only one asked question.kindly repost other question.…

Q: P(A)=0.3, P(B)=0.6, A and B are indep, find P(AB'), P(A|B')

A: We have given that  P(A) = 0.3 P(B) = 0.6 If A and B are independent then, P(AB) = P(A and B) =…

Q: Are the functions f, g, and h given below linearly independent? f(x) = et – cos(5æ), g(x) = e* +…

A: The functions are linearly dependent :