L-1 (s- 2)2(s 1)/ a. 4e2t + 4te?t b. -4e2t + 4te2t + 4et – 4et C. 4e2t d. -4e2t 4te2t + 4e² 4te2t 4et

Q: (2у? + 4л?) da — rуdy — 0 - %3D

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Q: r4 & 2Vz& /4z=x? 2. JJJO & 0 & 0 Jo & 0 & 0 S dydxdz

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Q: f(r, y) : = V3x? + 4y? fz(3, – 2) =|

A:

Q: dy If dæ 4x³ + 3x? + 6x and y = -3 when x 1, fınd y. |3D

A:

Q: dz a) $. Y z – 10

A: As per rule of bartleby we can solve only one question at a time and we can solve only three subpart…

Q: f(t) = 2t² + 4t – 3 4+2s-3s? А. c 4+4s-3s? С. s3 2+2s-3s2 В. 2+4s-3s2 D. s3

A:

Q: 4. (D² – D – 6)y = 0; when x = 0, y = 3, y' = -1 %3D

A: Use this auxiliary equation and complementary function

Q: ay is 8. If y = arccot then dz a. 4 b. 64 C. -4 d. -64 16 +x 16 + x? 16 +x .2 16 + x?

A: topic - derivative of a function

Q: EX. (D* – 5D³ + 6D² + 4D – 8)y = 0

A:

Q: 3) 2хydx + (y? — х?)dy — 0

A: The given equation is of the form Mdx+Ndy=0where M=2xyand N=y2-x2to check the given differential…

Q: (2st +t²)ds – 3s²dt = 0,when s = 1, t = -1 8st³ = (s – t)² o s³t = (t – s)* o 8st3 = (t – s) o t =…

A: To solve the given differential equation problem.

Q: D. Evaluate et-2 tan vE 2t + 3 S 't² – 2t + 1 e2t

A: To evaluate: ∫et-2e2t, tan tt, 2t+3t2-2t+1dt=∫et-2e2tdt, ∫tan tt dt, ∫ 2t+3t2-2t+1 dt+A,B,C

Q: ($4y - 7y–12 dy. y' +y? - 6y Q.4 Evaluate

A: We have to use partial fraction to separate denominator and then take integration to obtain…

Q: dy If y = e5z+14 then- dr O 5e5z+14 O 70e5z+14 O 4e5z+14 14e5 14 O 6e5z1 14

A:

Q: a. y" – 6y' + 9y = t?e3t, y(0) = 2, y'(0) = 6 b. y" – 4y' + 3y = 6t – 8, y(0) = 0, y'(0) = 0

A:

Q: EX:- Show that f dw = VE Terfcb) -erf ca] (ntb dw = E [erfcb) -erfca)] (ngby. Sol:- 9. ē" dw 2. Ff…

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Q: 2r² + 3sr - 2r t6s)s t s(st 2r -1) dr = 0 %3D

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Q: v(t) = t² – 3Vt, s(4) = 9 %3D s(t) = 2t 11 %3D - 3

A: Given query is to find position function.

Q: | 2y13-2y? dy?

A:

Q: Ve da 6. Given x=- 1 a = 3x +2x-1 and and y=- find 2 de c-4

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Q: Find d?y/d?x from x=t2-3t+4 and y=t2 +4t -5.

A: The parametric equations are x = t2-3t+4 y = t2+4t-5 To evaluate: The expression of d2ydx2 Formula…

Q: dy 4. if y = csch-1 2º . de

A: "Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: (2st +t?)ds – 3s²dt = 0,when s = 1, t = -1 8st3 = (s – t)? s³t = (t – s)* %3D 8st3 = (t – s)³ o t =…

A:

Q: (c) de xy³, y(0) = 1

A: Solving by separable method we can get

Q: X-2 +3t 9=1- 5t Ze 4+7t ? ans. d= o

A: The given question is related with the distance between a point and a line. Given a point P12 , 1 ,…

Q: d?y Find , if y = (60)tª + csc (5t2- e10t) + In (2t² + 3) dt2

A: To Determine: find d2ydt2 Given: we have y=60t4+cosec5t2-e10t+ln2t2+3 Explanation: we have to…

Q: I dz it ;C:又(t)=a+re ;ort S2下 2-a.

A:

Q: z+2 dz I cot (z?+4z-3)

A: ∫z+2cot(z2+4z-3)dzSubstitute u=z2+4z-3→dudz=2z+4→dz=12z+4du=12∫1cot(u)duWe know that…

Q: dy 2 = -5 : glo) = 1 y(o)

A: In this question we are given variable separable first order differential equation with initial…

Q: F(s)= 2s+8s+12 f(t)=?

A: according to the question we need to find the inverse Laplace

Q: Write equation for each ellipse.

A:

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: If x = t² and y = t³, then y O t 3/4t O 3/t Other: = ?

A:

Q: f(t) = 2t2 + 4t – 3 4+2s-3s? А. 4+4s-3s? С. s3 s3 2+2s-3s2 В. 2+4s-3s2 D. s3 s3

A:

Q: (a) E= 1.5x10-12 J, Q = 1.6x10-19, V = ?

A:

Q: -5 d (b) / (100 – |17|)dæ (c) dx In(w² – 1)dw) 5

A: We have to find the given integral.  For this we will use the properties of definite integral and…

Q: dy Given y = 2u? and u = 8x – 1, then dx - 8(64x? – 2x + 1) 0 خيار 4 48(8x – 1)2 0 خيار 3

A: The derivative of xn is calculated using the formula, ddx(xn)=nxn-1 .

Q: = -4rt ; when t = 0, r = ro 1. 2. xyy' = 1+ y? ; when x = 2, y = 3

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Q: d. deav ニ Gcv whin s-1, v = 3 ニ う

A: Answer only D

Q: メP d4-ex+5y, Where y=0 when x=O

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Q: 4. (D² +D-1)²y = 0 ,when x= y = 0 , y' = y" = 1, y" = -1

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Q: dz and dz if rys + y2³ + zr³ = 7. Find

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Q: If 2= 4y and if y = 4 when x = 0, then y = dx a. 4e4* b. e4x c. 3 + e** d. 4 + e4x e. 2x? + 4

A: Topic:- application of integration

Q: y? dy 4-7 2.

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Q: L:x = 2 – t, y = 3 + 4t, L2: x = 4t, y = 1 – 16t, z = 4 – 8t z = 4 + 2t

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Q: c) y" + 2y" = 32e²ª + 24x, y(0) = 6, y'(0) = 0, y″(0) = 14

A: Since the student has posted multiple questions and does not mention any specific question, so we…

Q: C' (t) = (20t + 28) /2.5t² + 7t, for 0 <t < 15, %3D

A: Solution

Q: зв. | Evaluate ф. - dz where C:z-2| = 2. (z³ – 5z² +8z –4) 3

A: