3. 4x – 2(x + 1) = -76 abnoa %3D

Q: D Exponential Shifting Theorem 4 (D° + 4D°-3D - 18)4=24x°e-3× t 4D²-3D - 18)y = 24 x°e¯*

A:

Q: 7. Differentiate a) f(x) = ev==t and b) h(x)= (5x² – 8r)e**-4". %3D

A:

Q: 3. 2t t dt ST-t

A: To integrate the given vector function. ∫te2t, t1-t,11-t2dt...(1)

Q: 1 7) Find the antiderivative: S 3x2-6x+12

A:

Q: 9. y = x – 5x+52) 21n10. y = 2r2 11. f(x) = 12. f(x) %3D x² +x- 6 15x2 +31x + 1 13

A: Since you have asked multiple question, we will solve the first question for you as per our guide…

Q: 10) W 3x -4 M x+3 • 2021 Kuta soft ware LLc. AIl righis reservet Made with Inf inite Geomery. 11)…

A: In a parallelogram, opposite sides are equal to each other.

Q: Solve the initial-value problem. 2хy' + у %3D бх, х> 0, у(4) %3D 16

A: Here, the given DE with the initial condition is: 2xy'+y=6x, y(4)=16

Q: x = c, e" + cz e- 21 e" O x"- 2x'- 3x 8 e O x" + 2r'+ 3x = 8 e' O x" - 3x'- 2r 8 e O x"- 2x'+ 3x = 8…

A:

Q: Example: Solve: y' + 3y = e' (1) By Integrating Factor Method:

A: Given data:   The given differential equation is y'+3y=et.   The standard expression for the Linear…

Q: S(3x + 5)e3*+5 dx D 1 e3x+5 3 (3x +4) + C 3x+5(3x + 6) + C B)e C) e3*-5 (3x + 6) + C D) e3*+5(3x –…

A: Using substitution method of integration & By parts rule

Q: 12 - y+ ] - dy = |+C

A:

Q: In z dz z4 e

A:

Q: d. yı = X1 X3 X1 + X2 Ya = - X1 – 3x2 – 2x3 e. yı = x1 + 2x2 + X3 Y2 = Y2 = x1 + x2 Ya = X2 + X3.

A: d)  The map from R3 to R2 is onto.  e)   The map from R3 to R3 is not onto.

Q: 1. y" + 4y' + 4y e-2x x2

A: The given differential equation is: y''+4y'+4y=e-2xx2 Now the characteristic equation of the…

Q: х4—х2+1 - [3] S [3] s e*ve*-1dx еx+3

A:

Q: (e) Yk+1 +Yk = 1/k(k+1),

A: Given, yk+1+yk=1kk+1Substitute:yk+1=y'yk=yEquation formed is:y'+y=1kk+1A first order separable ODE…

Q: If y=x* - 5x² + 2x – 3 then equals dx A x* - 5x² + 2 В 4x – 10x+ 2x – 34 4x - 10x+ 2x D 4x - 10x+ 2…

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Q: What is the value of m if y=mx<-2x-3 has a critical point at x=-2?

A: Given y=mx2-2x-3

Q: Solve the initial-value problem. 2xy' + у %3D бх, х> 0, у(4) %3D 20

A:

Q: ydy 1. S- V25-16у* xdx 2. S- 9+x 2 dz 3. S- 2 +6z+10 xdx 4. S- 9+x

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Q: What happens to N(t)=100x e^(5t) as t → infinity? Based on your answer would you consider this a…

A:

Q: 3. Solve the following using Two Phase Method MIN Z = x1 + x2 subject to 2x1 + x2 >= 4 x1 + 7x2 >= 7…

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Q: Evaluate (D^2 - 3D + 2)y = (1 + e^-x)^-1.

A:

Q: 8y dy e2y

A: topic - definite integral

Q: 11 FCF)dt= fCx) dx =- 43 then 1.

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Q: Evaluate the integral

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Q: CV4-x2 4-x2-y2 1- o So Si s** ydzdydx Jx²+y2

A:

Q: Find the general solution of xy²dx = e

A: By using variable and separation method

Q: S * x3 (2x+5-3Wx)dx 0월 18-52-28 100 +c 0 23 5 +5x³ 8x³ +15x² - 2 +c +c ○ 2x35x4 22 5분 28 +0 + 5 4 3

A:

Q: 6-9 d x.dy 2.

A: A double integral is given. We need to evaluate the double integral.

Q: 7) (1+x²)dy+2.xrydx = 0

A:

Q: 3(1 + P) = 2ty(y³ – 1) dt %3D

A: Let us consider the differential equation dydt+P(x)y=Q(x)yn It is known as Bernoulli's equation…

Q: (1+x2) y' + 2xy - 4x2y3 = 0 (Bernoulli)

A:

Q: S(x)=-2x+8x S(3) = %3D S(-1) =

A:

Q: 2 1) x² + y² + 18x - 26y+246=0 CX+972+(₂-137² = 4

A: As per the guidelines we are supposed to answer only one question at a time. If you want answers of…

Q: - EXAMPLE 3 Find the particular solution of 3xy' y = lnx + 1, satisfying y(1) = -2. x > 0,

A: It is a first order differential equation.

Q: (1) In(x - y) = xy + y³ ;

A: According to rules, I need to solve first question.. Please repost remaining questions

Q: 4 %3D X2+2x-15 is X-3 S+X

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Q: S(6 + 6y – y²) dy

A:

Q: 1. y" + 4y' + 4y = e-2x %3D x2

A: We find the complementary solution Yc and Particular integral Yp The complete solution is sum of Yc…

Q: •7 49–x² r83–x²-y² x dz dy dx %D 0, -15+x²+y²

A: I am attaching image so that you understand each and every step.

Q: -2x X-e -2x x+e * 2(x-e-2*) A -2x xp- x²+e¯ -2(x-e-2*) B x²+e =² -2x -2x e dx -2x x²+e-2r x²+e=2« D…

A:

Q: b. y = e-2x @x, = In 2

A: Solution

Q: ral of the d D- 1)y is

A:

Q: Find the general solution of the DE y" + 4y + 4y = e²x

A:

Q: Find (5x - x²)e* dx O(x2 -5x)e-x-(2x - 5)e¯X – 2e-*+c O (5x-x2)e*- (5 – 2x)e* +2e* O (x2-5x)e*- (2x…

A:

Q: 2 4 Mx(t) = -e+ 3t e' + e" + %3D 3 15

A: Given: Mxt=13et+415e3t+215e4t+415e5t

Q: , у"+ бу'+ 9у 3D 0; x = 0, y = 0 and x = 0, y' = 3 = Ans. y=3 x e-3*

A:

Q: Find an antiderivative. x² + 1 x2 - 5x - 6 |

A: Antiderivative means integration. Here, the method of partial fraction is used for integration.

Q: ∫ 3e^(5t) dt

A: The given integral is ∫3e5tdt