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Q: y= e fonksiyonunun d'y dy 11 + 27y = 27e dr 11z dr?

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Q: y" – 7y' + 12y = 3t?e4t – te3t sin t -

A: Given:  y''-7y' +12y =3t2e4t -te3tsint

Q: Given z= 10t +43 and y = 65t+143 %3D %3D dr (i) dt dy (ii) dt %3D dy (iii. (write the simplified…

A: Explanation of the answer is as follows

Q: finn D2:- knowing thet fcxy,Z)= tavm of C in dx そ= X+y Z= X

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Q: - 1 for Ye Y, Give Ex pre ss im an

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Q: Consider the two quadrature rules 0 Which one is better? Þƒ (¹) +cf (1), 2 3 + ߃ ( ¹² ) + yf าร์ (…

A: The function f(x) is integrated from 0 to 1.

Q: dy Find for the following by using appropriate rules: iv. x² + y3 + (lnx)e♥ = 4. y = Vx(3x2 – 1) V.

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Q: - y² + 22 = 169 at (5,0,12). %3D (1) . i+3 3 3 -) i+ k, 6. 12 12 =) i+k, (d) k. i+

A: In this question, the normal to the curve is calculated using the finding gradient of the function.…

Q: (v) er-y de +e**"dy = o

A: We will solve the differential equation by the method of separation of variables.

Q: Hawis Find d Vand V2if vI+2V2=31-k and 3V-V2 si+j+k

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Q: S Sz(x² + y³)dxdy, wherein B = {(x, y) E R²; 0 < x² + y² <4}.

A: Double integral

Q: d?y 13 으18 + t6/3- t2 + 246 3 Find if y(t) - dt2 3

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Q: R. 4. Use the information in the figure and prove that VC = CX, making use of reflec- tions. [UCSMP,…

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Q: Solve : dy- (- y) . Inn dy %3D ,13-1 Ordinery Dibberential equetion.

A: Solution:Givendydx=(1-y13)x2 ln xy13-1

Q: TF x and y are orthon ormal rectors then Pind Value of Ilx+y12 - ||x-Y2

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Q: e where r is jiven peu'ametor! Fnd f'6).

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Q: Q.2 JJR ex2-2 dxdy, where R between x2 =-y, y = 0 and x = -3 , y = -9

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Q: dx Cane:2e-25x

A: 13)

Q: Q2) If y(0) = 0 and y'(0) = 0, ƒ (t) = e*t, %3D 1 y(t) = (D + 3)(D + 2)(D + 1)ƒ (t), determine y(t).…

A: Here first calculate differential part.

Q: There does not exist r E Q ə r² = 2 ylgn ihi

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Q: "x is between c and d" translates to csxsd O True O False

A: Given query is to find statement is true or false.

Q: Hi W. Solne : du 니 メ Uco,y) = 3ē_ = 34 ニ e | dy Xープ Ans./ ucx,y) = 3 e (2x-5y) 131

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Q: C is given by x = 4t and y = 3t, where t runs from 0 to 2. Evaluate (y/x)ds 45/2

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Q: . In WXYZ, WX = 10. What does ZW equal? %3D а. 16 b. YZ с. WY d. none of these

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Q: ,-(ax²+2bxy+cy²) dædy = e (Hint: Let s = x+By and t = yx+8y, where (ad – BY)² = ac-b². Then ax?…

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Q: dz, C:z| = n. %3D 2++13z2+36

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Q: Q3:A/ Find: dy dy y 2 Vy (1 + Vý)² yV4y? – 1 |

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Q: z)dy + (y -y of the triang Land (0 o 6)

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Q: dy de y =(x-1)(x+1) If x=3 equals ? then

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Q: d²y Given that x3 + y³ = 2, prove that 4x dx² y5

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Q: Frd he e of teepkan in the at quectert baurded on he let ty he ydx, bebw by tte carve x- boletby…

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Q: LaS xsin(y?)dydx 1-

A: As per our guidelines we are supposed to answer only one question because there are multiple…

Q: dy Find dz given that y = -2 – 8z². z=-3

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Q: 10 dz where C2 is the top half C2 that is C2: |2| = 2 with z = re", 0 < %3D

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Q: 5. (D2 – 5D + 6)y = 18x2 + 12e2* (Assume yp = Ax² + Bx + C + Ee2x)

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Q: Supposo that | FC) dx =13, fい)n -23, and gla)dx=35 2. fCx) drx = こxp(の J3fa) dx= C+fし),33J- 2.

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Q: dy If y e+14 then- dz 70e+14 O6e+14 D 4ez+14 O 14ez+14 5ez+14

A: Given, y = e5x+14  We have to find dydx

Q: dy **+y = xy? ii. .2

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Q: the firs YS he ghuen von Costt)-d

A: Given functionf(x,y)=∫yx cos(t2)dt

Q: J(y) = S. [(2x – 3)²y? – 6y²] dæ, - 3)²y2 – 6y²] dx, Y € C²[a,b] Find

A: Given:

Q: 7 dy (18a* + 16e5)', find da Given y = %3D

A: It is given that,

Q: (D - 2D + 4)y = 0 ; y= - 2, Dy = 8, D²y = 0, when x = 0.

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Q: Jv²esc?(y³)cor²(y³)dy, we let u = cse(y³) A True B) False

A: To solve the following integral by substitution

Q: BD = 10, GF = y, AC = 4, AF = X %3D %3D y D

A: From the given figure BD=GE And Chord of equal length are equidistant from centre  Therefore, AF =…

Q: f (г, у) — In(ax + by) a, b ER af Land 1 Find Ja 2. Find and a f -and 3. Find dxðy дуда

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Q: y? dy 4-7 2.

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Q: Q2: Given y = f (u) and u g(x), find dy/dx: y = 2u3, и %3D 8х — 1

A: Differentiate

Q: Determine the order of the DE. а) y' + у %3D 5у? b) = t dy dt c) y' = y" + 5t2

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Q: Evaluate ſ z dz, where C is given by x = 3t, y =t²; –1<t< 4.

A: Let us consider a complex function f(z) then the function can be written in the Cartesian coordinate…

Q: Q2: y" + ay' + by f(t) Find a,b and f(t) so that Ypı = et +t? – 1, Yp2 = e2t + t2 – 1

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