1 (a) y= %3D - (b) f(x) = 3(r³ – e²) %3D 4 (c) h(x) = 3x³. %3D

Q: (d) (x– 2)* + (y-9)* =1 (e) x² + y² = 1 (f) x² +(y+5)° = = 25

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Q: y" + 2y' +y = e-*

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

Q: V121–a² r85-x²-y² 11 x dz dy dx -157+x²+y²

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Q: 6. S -3dy 2y2+14y+70

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Q: y′′ + 2y′ − 8y = 2e-2x − e−x , y(0) = 1, y′ (0) = 0.

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Q: 5T 1 y=-2cos(Gx+っ)+1

A: Phase shift: -5π

Q: fx=å (3in (x*ry)-x2) %3D fy = Ly(31n (x*+y)-x2) %3D d fe-(3in (x*ry)-x2)

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Q: determine L−1[F].

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Q: X1, X2 2 0 12. Minimise Z = 60x1 + 80x2 bo Subject to 20x +30x2 2 900 40x1 +30x2 2 1,200 X1, X220 LO…

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Q: xy = e2x; y 2х ху — е

A: We will find y' as following.

Q: y''-3y'+2y=5e^3x,y1=e^x

A: Reduction of order is a very significant and basic method to solve higher-order linear differential…

Q: 2 + x², -2 < x < 0 f(x)dx; f(x) TX + 2, 0<x<4 21 -2

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Q: r/64–x² r61-x²-y² x dz dy dx -67+x²+y²

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Q: [g(x )cx = 2 If then g(x )dx equals

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Q: Resuelva yDx - 2(x+y) Dy=0 O x² + 2y = cy² Ox+2=cy² O x + 2y = cy² Ox+2y=c

A: Given differential equation y D x-2(x+y) D y=0 The objective is to solve the differential equation.

Q: let x= et then by the chain rule d3x/dx3 equals

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Q: A) xy' 2y + x'e*

A: These are all unrelated &amp; lengthy problems. By Bartleby policy I have to solve only first one.

Q: E (X² + Y²) E (XY)

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Q: 2 c4 e-x-2y dydx 2х

A: It is double integration problem

Q: 3. /4(1-)esc (1-y)dy

A: We have to solve the integral

Q: ) y( 3x*- xy - 7)d -x ( xy ty- 2x) dgy = 0

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Q: 2y´´-5y´+3y=0   y1=e^x

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Q: Evaluate VA-x2 4-x2-y2 (x² + y²) dz dy dx. -V4-x2 0.

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Q: y" - 2y' + 2y = e'cscx

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Q: 22. y = 3* 23.) f(x) = 24 fx) =x %3D + 4 2x + 3 g t) = - 7 fx) = 7x – 4 7x- 4 %3D 8(x) : %3D %3D

A: As per bartleby guideline for more than three subpart question asked only first three is to be…

Q: y" + 4y' + 3y = 15 e^2x + e^-x

A: Given differential equation is: y''+4y'+3y=15e2x+e-x Solution of differential equation is sum of…

Q: y"-2y'+y = e* Inx

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Q: S Ve3x dx A 2 X- e3 2. C + C ez* + C - 1 e3x + C 3. + C - 3. 23 B

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Q: In the function given. Evaluate the integrals.

A: Given:∫03 fx dx=2,∫36 fx dx=-5∫36 gx dx=1∫36 3 fx -gx dx=?

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

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Q: 2y''' - 3y'' - 3y' +2y =(e^x + e^-x)^2

A: We have to solve the differential equation  For which we first solve the homogeneous equation and…

Q: Fresh fish (MC = 78%) is sold at 60 pesos per kilo when acquired in bulk manner. If it has been…

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

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Q: x-e -2r -dx x²+e-2« *2(x-e-2«) A x²+e-2r xp- – 2(x-e-2x) dx x2+e-2r B -2x 2+e =21 dx x²+e-2¢…

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Q: 1 S² = y e2y dy

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Q: d^x 2: +3. db4 3d ³ x db³ d²x -62 dx - 24x=0 db 27. db²

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Q: ly₁ dr dy₂ 2t = y₁ + 4y₂ + e¹t - e²t = y₁+ y₂ +t+2

A: given  :         dy1dt=y1+4y2+e4t-e2tdy2dt=y1+y2+t +2 We have to solve the given system of…

Q: 4. Suppose y = 3x + 2. What is Ay if x increases by 3?

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Q: a) | f(x)dx = -10 %3D 4 b) f(x) dx = -10.5 4 c) f(x) dx = -17.5 10 d) / f(x) dx = 9 %3D 10 e) -5…

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Q: 6) y = e *(x* – 5) dy A) dx 5x² 10x + 4x3 = 21(5e* + 2x²) dy 5x2 B) = e* · 10x · 4x³ + e³* · 10x ·…

A: Let h(x) = f(g(x)) for all x, then by chain rule   h'(x)=f'(g(x))g'(x)  Also if h(x)= u(x)v(x)  Then…

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. The second derivative of y = e3* + e4* is + 4e4x b. 9e3x + 16e4* а. 6e3x + 8e4x d. 9e9x + e16% C.

A: The given function is: y=e3x+e4x

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…

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Q: 2x+y-52 +l =. X-y+ 2-6= 0 4x+zy-32+8 =

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Q: So Ve Pollowing the D.E 3X 3y' = e - \2 X +39

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Q: 4s+2 1. F(s) = s² +6s+34

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Q: x - 1 = λχ y = 2 = λy z = -λz (x² + y² = z² = 0,

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Q: y = (2x + 1)v2x+1

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Q: D’(D² – 4)y = 3x+ 2e¬3* | y = 3x + 2e¬3x m° – 5 - 4m³ = 0 ® m' (m2 – 4) = 3x+2e-3* D (D² - 4) = 0 3…

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