FI = r Where f(r) = -i = 2xi – 3yj + zk So be it %3D div) grad(f) find

Q: 2x +3 What is the actual du to be applied when integrating / 3x -7 dx a. x2 +3x -7 b. (x + 3) dx c.…

A: ∫2x+3x2+3x-7dxLet u = x2+3x-7dudx = 2x + 3 du = ( 2x+3 )dx ∫2x+3x2+3x-7dx →∫1udu= ln (u) + c= ln (…

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Q: If x-0.78 and y 0.83, then value of Cin the antiderivative of F(X)= xsin-(x) is V1- x2

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Q: SOLVE USING INTEGRATING FACTOR (2y² – 3x²) d x + (2x² – x y) dy = 0; y (1) = 1 9.

A: Let's find.

Q: Use integrating factor to find the general solution of y' /(x2 +1) = 3 − xy

A: A first-order linear differential equation has a standard form of y'+P(x)y=Q(x). This differential…

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Q: B. Integrate the following using the basic rules of integration and substitution. 1. fx² + 5x3 –x-3…

A: Given problem:-

Q: function fo) = 7X1+10x10x3_4 Qn Antiderivative of fo) is F(x) = Axn+ Bxm, CxP+Dx: A= 710 %3D where…

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Q: -. Evaluate f³ exp(ar)dr where a > 0

A: Evaluate the integral which is given as, Integration of ex is ex and differentiation of xn=nxn-1…

Q: (test for exactness) (2ysinxcosx - y + 2y²e*v¨ )dx = (x - sin'x - 4xyev" )dy %3D

A: Given DE is 2ysinxcosx-y+2y2exy2dx=x-sin2x-4xyexy2dy Test the exactness of the given DE.

Q: 5. Test the exactness of ODE, if not, use an integrating factor to make exact and then find general…

A: Differential equations

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Q: Integrate Ix(x 2 +5) 7 dx by using substituition method * (2x+5)* +c (x² + 5)* 8 +c 16 (a² +5)' (2a…

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Q: i $ 6x³e**+3 dx. Using integration by parts (S udv = uv – f vdu) and letting u = f(x), dv = 3g(x)dx,…

A: Using integration by parts

Q: Coefficient Linear in Two Variables 2. (x – 3y– 7)dx – (2x –4y-8)dy =0

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Q: Sx + 2y = 0 xy = -2 (x, y) = ( (smaller x-value) (x, y) = (larger x-value)

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Q: dx² +2dy - 5y = 2x²-3x+1 dx

A: Given differential equation is d2ydx2+2dydx-5y=2x2-3x+1 So, the auxiliary equation is…

Q: Write the general antiderivative. (Use C for the constant of integration.) x2+1 dx 5x Need Help?…

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Q: Coefficients Linear in Two Variables (x +2y - 4)dx + (2x + y-5)dy = 0 when y(1) = 0

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Q: Integrating factor method dy/dx -2y/x = 3x^2

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Q: Integrating factor method t (dy/dt) +2y = t2-t+1

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Q: B. Integrate the following using the basic rules of integration and substitution. 1. fx2 +5x-x-3 dx…

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Q: 2-/2x+1 Let F(x,y) = C be the antiderivative of f(x) = What is the value of C if x=11 and y=20 ?…

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Q: Solve using Integrating Factor by Inspection. Show Complete Solution. y^2 ( 1 − x^2 ) dx + x ( x^2y…

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Q: 2. [f 5y ey dA, F- {(x, y): 0 s x s y?, 0 s ys 2} F

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Q: > > f(x) = 2x * d F(x)=(√2x+2/2) f' X+ dx f(x) = , (Vzx) = dx 2√2 x لعلم قواعد العاه م حسب الم d |…

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Q: 3. y = x³ – 3x² + 2x – 6 ACTIVITY 1. Find the deriva 1. f(x) = -2 2. g(x) = 4x3 %3D 2 %3D -

A: Solution:As per our guidelines we are supposed to answer only three questions. Here  f(x)=-2

Q: It represents the integration factor of the equation y (2xy +1)dx +x (1+ 2xy -x'y'dy = 0 al Jusi…

A: Given

Q: 1. (12 –2ry+6x)cdx- (r² -2xy+ 2)dv= 0 |

A: First check exactness then solve

Q: General solution using Exact method. x^2 y dx + (1 + x^3) dy = 0

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Q: C. VARIATION OF PARAMETERS 2. (D² – 3D + 2)y 1+e-x

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Q: 8y2 + 3 dy /6 – 2y

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Q: xsin-(x) If x =0.03 and y = 0.62, then value of C in the antiderivative of F(x) = is V1-x2

A: Given  F(x) = x sin-1(x)1-x2

Q: (2х + Зу — 5)dx+ (3х — у — 2)dy %3D0

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Q: Solve using Integrating Factor by Inspection. Show Complete Solution.…

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Q: Integrating factor for xy dx + (2x2 + 3y2 - 20) dy = 0

A: topic - integrating factor of differential equations

Q: Integrating Factor by Formula b) y² cos xdx + (4 + 5ysinx)dy = 0

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Q: y (x 2 + y 2 – 1) dx + x (x 2 + y 2 + 1) dy = 0

A: First find integration factor then solve Using formula

Q: Integrating Factor by Formulas: (4) (4xy + 3y² – x)dx + x(x + 2y)dy = 0 (5) y(x + y + 1)dx + x(x +…

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Q: using variation of parameters: - 2x + x = e t (et 1 1)2

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Q: HX T-Th HY 3)1+2 2. 14 the eavation

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Q: Integrating Factor by Formula b) y²cos xdx + (4 + 5ysinx)dy = 0

A: Given: y2cosxdx+4+5ysinxdy=0 An equation of the form Mx,ydx+Nx,ydy=0 is said to be exact if…

Q: Use integrating factors to solve (x² + y² + x)dx + xydy = 0. %3D

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Q: A. By simple integration rules 1. fki+3x-2 + 5x+)dx 2. s**-5x²+4x dx (x-1) 3. S*- x3 -343 dx X-7 4.…

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Q: The integrating factor of XInx +y=2Inx dx Select one: а. In2x O . Inx С. O d. In3x

A: Given differential equation is xln(x)y' = 2ln(x)

Q: valuate dy and A v for v = f(y) = x2 -6x +35 x =4 and dy = Ax= 05

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Q: O fi[0,00)→R all continious Aunction aro Sx³f(x') dx = Sx f(x) abx %3D show this.

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Q: linear integration where product C:y = 2x, 8i Cr²+y)dx + (Zxy +3)dy

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Q: integrating factors. 3. y(xy + 2)dx + 2xdy = 0

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Q: The product of the triple integration he * *+ y² + z*)$ dzdydx (x² + y² + z²)î dzdydx The product of…

A: To evaluate the below integral. ∫03∫09−x2∫09−x2−y2x2+y2+z21/2dzdydx