CALCULUS 1 DIFFERENTIAL CALCULUS x2-8x+7 5. y x2+4 dy dx

Q: dy :- (x + 1)y = xy² dx

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Q: (D³ - 7D + 6)y = 0 %3D

A: Differential equation

Q: Formation of Differential Equations by Differentiation and Combination Y = cze-2* – 2c2e* - 2cze*

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Q: (D³ - 3D² - D + 3)y = 0

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Q: Differentiale and integrate Hhe ff. power seties. 1) fx): n=0 2n nr4 (3n-4) x 2.) f (x)-= n=1

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Q: Verify the identity.

A: To verify: The identity . Formula used:

Q: x-2-x-4 The differential of y= x-2-x-3 is

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Q: 2. Approximate V63.

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Q: Differential Equations  a) x''+x=0 b)x''+16x=0

A: Given differential equation is      X" +X=0-----(1)    L(X ") =S2 ×(s)-Sx(10)-X'(10)    L(X) =x(s)

Q: Linear Differential Equations (20) 3xy' – y = In(x + 1)

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Q: Differential Equa y= Co 作=A y = 2x y- xy-2y = 0.

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Q: Linear Differential Equations (19) + 3x?y =

A: First I have written the standard form of first order linear differential equation and then using…

Q: 2+ ye*y y' = 2y – xe*y ху %3D

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Q: DIFFERENTIAL EQUATIONS (x2 + 1)dx + x2 y2dy = 0

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Q: lim (x,y)→(0,0) r sin² y + y sin² a x² + 3y²

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Q: Exact Differential Equations (2xy + 1)dx + (x² + 4y)dy = 0 (18) (6xy + 2y? – 5)dx + (3x2 + 4xy –…

A: First I have written the definition of exact differential equation and it's solution rule, just use…

Q: Differential Equations  a) y''-2y'-3y=x+1

A: step 1: Gievn:y"-2y'-3y=x+1and y(0)=1        y'(0)=1then, find the value of y(1)=?so we know…

Q: Elimination of Arbitrary Constant - DE (y-x)^3=cx

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Q: Evaluale tim xin xs

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Q: +2)

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Q: x(y-1) alx=y(x=1) dyso

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Q: II. DIFFERENTIATION 1. (E- 2x) = A- 2 B.는-2 +2 D.-2 %3! 2x 2x-1 2. 21

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Q: 10x* – 18xy2 + 10y³ = 48 %3D

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Q: b. xy' – v = x In v. Y(1) =

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Q: d'y 6x2 dx2 dy + 2x - 3y = x'e2"; dx

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Q: EXAMPLE 7 Finding Differentials of Functions (a) d(tan 2.x) = sec² (2.x) d(2x) = 2 sec2 2x dx (x +…

A: (a) dtan 2x=sec22xd2x=2sec22x Hence the answer.

Q: 5. y" + y = = sec x tan x

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Q: Sinhu.Coshv =1/2 [Sinh (u+ v) + Sinh (u- v)]

A: Sinhu.Coshv =1/2 [Sinh (u+ v) + Sinh (u- v)]

Q: Differential Equation Solution x² + y² = Cx 2xyy' = y² – x? x² + y? = Cx Y(x)= C1sin 2x + C2 Cos 2x…

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Q: Determination of Integrating Factor Solve (x3 +y2)dx + (x2- 2xy)dy = x3 + 2xy - 2y2 =c O x3 - 2xy -…

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Q: linear differential equation  xdy+2yx^2dx+ydx=5xdx

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Q: =x+6 Line 1: y= 2 Line 2: y=x-1 =-x LI

A: In system A, L1:y=x+6L2:y=-x The graph of the lines are intersect at one point. Hence there is…

Q: 3. (2 + 5z) e* dr

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Q: 1/2 dx 1-х4

A: Let 1-x4 = t

Q: dx 3. dy x²+2xy y?

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Q: d'x d²x dx + 7x = 3 sin 8t. dt 5. +2. dr3 dt2

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Q: | (3t + t*) sin(2t) dt 3.

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Q: ,3 dx (x2+а2)3

A: Given integral is: A=∫x3(x2+a2)3dx                   (1) Use substitution method to solve this…

Q: Их + з луз, му и (x,0) 3 zo

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Q: Subject: Differential Equation Topic: Coefficient Linear in Two Variables 1. (2x - y)dx + (4x + y…

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Q: Evaluate: e*dx X Ve2x

A: In this question we have to find the integration.

Q: イナ dx メーよ

A: Given :∫12x+1x-5dx

Q: Differential Equations Solve: dx + y= sin t dt dy + x cost dt where y (0) = 0, x (0) = 2

A: We have to solve dxdt+y=sintdydt+x=cost    where y(0)=0, x(0)=2

Q: Differential Equations  a) x''-2x'-3x=0 b) x''+4x=cos(3t)

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Q: sec-1(V2+h)-sec-1V2 (ii) ļim h-0

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Q: dy Vy+4-2

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Q: Calculus 11th Edition - Ron Larson Chapter 3.9 - Differentials Please show all work and explain…

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Q: Y"'-y"+y'-y=xe^x-xe^-x+7 By using differential operators methode

A: To solve by using differential operators method.