7. J -12 у-13 dy (2у +1) (у-3)

Q: Find the general solution of thedifferential equation. (2+x)y'=3y

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Q: 4. dr/dt = -2tr, r(0) = ro %3D

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Q: dP 5. = P- p2 cet Ans: %3D %3D dt 1-P

A: topic - differential  equation

Q: у" — бу' + 9у %3 t'e", y(0) 3D 2, У (0) 3D 17

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Q: d²y dy – 4 + 4y = e2t.t dt2 dt

A: our objective is to solve the differential equation

Q: y' + z' - 2y = 1 z – y' = t %3D Yo = 20 = 1 %3D -

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Q: 2x –1 1 , show that y"+ y' + xy +1 c) If y =-

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Q: Solve Ytt = = 4yxx 0 0 Yx(0, t) = 0, Yx(1, t) = 0, Y (x, 0) = 0, y(x, 0) = 3cos(2nx)

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Q: 5. St V1-t dt

A: We solve this integration by substitution method by putting                         1 - t3 = u…

Q: 6. J-3 0 + 4y +4) dy 1. 8. (3w2 - w- 1) dw 9. 10. 31-3 dt

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Q: 1-x² 2. , S. et²+y? dydx = (е-1) 4

A: We have to show that:  ∫01∫01-x2 ex2+y2 dy dx=π4(e-1)

Q: 26. у" + 4y' %3D sec 2x

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Q: Find d²y if y =x² +3x-7 and x=2t+1. dt?

A: y=x2+3x-7 and x=2t+1

Q: (금)시 3 k dt t2 (5 – 5t)i + 4/tj+ -

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Q: 2. (s-s?-t?)ds + (t + s? +t ?)dt = 0

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Q: 2 3 dt. 0 1+t2

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Q: t(s² + t?)ds – s(s² – t²)dt = 0 %3D -

A: We have,  ts2+t2ds-ss2-t2dt=0 On re-arranging and solving a bit furthermore, we get the result as…

Q: (2) + 2w = 0, dt %3D dt3

A: In this question, we need to find the order and linearity of the differential equation.

Q: Obtain 2 linearly independent solutions valid near the origin for x>0 2хy" + 5(1 — 2х)у' — 5у %3D 0.…

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Q: Find x and y in terms of a. X + y = 0 х+ ay %3D 6 (а + 1) (х, у) —

A: Given:    x + y =0        --------1   x + ay = 6     --------2 from 1: x = -y put the value of x in…

Q: 3 '9-x2 3+V9-a2-y? 1 dz dy x² + y² x²+y² a C = L7I Fle,0,6) dp dộ do

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Q: d²y dy +2 + 5y = 5t2 dt? dt

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Q: Compute (T2 T)(x, y). T(x, y) (3x, 7y), T2(x, y) = (x-y, x + y)

A: We have to find T2 composition T1 .

Q: find dy/dx

A: Known formula: ddx∫rxqxftdt=fqx q'x-frx r'x.

Q: 1 9 1 dt 1 + t2 %3D II

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Q: if y= 3t^2+t+2, x=(2t-3)^3 then dy\dt= 6t+5 false true

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Q: how can i find the vectorial equation for d1:3x/2=y-1 and d2:?x+y-6=0

A: Given: vector equation for  L1:   3x/2=y-1 l2  :   x+y-6=0

Q: .1//3 7earctan(y) dy + y? 3

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Q: Solve du a²u k xe (0, L), t>0 ôu (0.1)- ĉu (L,t) = 0 ди (0,1): Əx 87x - 3 сos L 3n x u(x,0) =…

A: Given: The given heat equation is ∂u∂t=k∂2u∂x2, x∈0,L,t>0. ∂u∂x(0,t)=∂u∂x(L,t)=0

Q: y'+2y/x=x, y(1)=2, y(2) using h=0.1

A: given :y'+2yx=xy(1)=2, y(2) using h=0.1

Q: dy dt = y(у — 4)(у — 8), до 20

A: see my solution

Q: y" + 4y' + 13y = te-t %3D y(0) = 0 y'(0) = 2

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Q: 3. p + y = ty dt dy 2ty(y – 1) dt 6. 3(1 + ²) %3D

A: Given 3 t2dydt+y2=ty6 31+t2dydt=2tyy3-1

Q: 1.) y = ,"(x* + )d. 3 1.) у 3 /1-х2, 2.) у %3D S Vu du

A: Newton-Leibnitz rule :                ddt∫g(t)h(t)f(x)dx=f(h(t) dh(t)dt   + f(g(t) dg(t)dt Note…

Q: z = 2 24 z=Vx² + y² 2 FIGURE 9

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Q: 14. dQ/dt + (2/10 + 2t)Q = 4 2(5 + t)² + C 5+t

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Q: 4 + 2y - 16) dy =

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Q: 1. The complementary equation to dt² + dy + 4y = 5e-³t is:

A: Solution is here

Q: 3. Obt nin the parh cular folu tion 9. xdx - ydx + 3x dy +ydy = 0 ; wun x - 5,4= -:

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

Q: If s = 4/t - 3, then %3D ds dt

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Q: 2 sec 0 r drde = x² + y² dydx %3D 0. True False Reset Selection

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Q: -4-sy=0, y(1)=0, y'(1)=2 b) dt

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Q: Calculate AB – 2CT where 1 2 A -1 0 1 1 2 1) В C = 0 1 (-3 2, -

A: Given the matrices A=12101-1,B=-1021-11,C=-21-32. Calculate AB-2CT.

Q: {6} = I ( (b) T = [4,9) %3D (c) T = [-4,9] -

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Q: d³r dz +t- dt3 (c) 4tx = 0 %3D dt

A: The solution is given as

Q: 19. tag³z dz %3D tag' z tag²z dz tag³ z (sec' z – 1) dz %3D

A: The given is to find∫tan5 xdx

Q: d²y(t) dy(t) + 8 dt + 25y(t) = 10u(t) dt2

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Q: y"+16y = u(t) – 8(t – 1), y(0) = 0, y (0) = 1.

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Q: 10 1 y = 5 dt y(0) = -1 = 2 ot

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Q: (42ª + 3y² + 2z)dV B = {(z, y, 2) | 0 < I < 10, 0 < y < 8,0 <z< 1} .

A: Let's find.