(3z²+5z+3)dz (z- 2)(z+3) Integrate:

Q: 4. If integration using u-substitution technique is used to solve for correct choice for u? (a) u =…

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Q: Obtain the solution using Integrating Factors Found by Inspection. 3.) 2x⁵y' = y(3x⁴ + y²)

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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: d²x dx 2 + 10x = e2t x(0) = 0, x'(0) = 1 %3D - dt2 dt

A: Given differential equation is d2xdt2−2dxdt+10x=e2t. and x0=0, x'0=1 Write the auxiliary equation…

Q: Find a homogeneous LDE with constant coefficients that has y= - 3xsin2x as a particular solution.

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Q: - y" + 5y' = 0

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Q: y" - 2y'- 8y = 2xe* %3D

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Q: Obtain the solution using integrating factors found by inspection ydx + 2(y4-x)dy = 0

A: Since you have posted a question with multiple subparts, we will solve the first three sub-parts for…

Q: ChainR ulef or PartialD erivativs

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Q: dy (х — 1) — у + 2(х — 1)3 dx

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Q: 2y +y .dy +1

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Q: (x – y²)dx + 2xydy = 0

A: We have to find integrating factor of given differential equation.

Q: Use the method discussed under Integrating Factor Method. (PLEASE SHOW COMPLETE SOLUTION AND WRITE…

A: We have to find the general solution of the given differential equations using the given information

Q: Find the integrating factor of y'+ 3(x^2)y = 4(x^2)(y^2)

A: Divide the equation with y^2.

Q: ydx — хdу %3D у?dy

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Q: Solve the Cauchy problem (do not use the method based on the integrating factor): 2y y' - (x + 1)³,…

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Q: integrate dy/(sb - smy-bny-nmy^2

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Q: 5. (x2 + y² + 1)dx + x(x – 2y)dy = 0, x = 2,y = 3 %3D

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Q: Svain2x dx =uv- fvdu - Svau. x/x In 2x- Vx dx v- Svau- Using Integration By Parts, Find uv- Jv du O…

A: Find your answer below

Q: dx -- 2 = 3y - 2 when x = 1, y = 1 dy

A: the given differential equation is: ydxdy-2=3y2-2 it is given that when x=1,y=1 we have to find…

Q: Fiven the following non-homogeneous system of first-order linear differential quation: у3 2у1 + уг +…

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Q: What is the integrating factor of 6y²dx (2a + y) dy = 0 %3D

A: A non-exact Differential equation becomes exact when we multiply it by an Integrating factor.

Q: T "cos(x²)dxdy? What is the reversed order of integration of 'y a. I T cos(x²)dydx ST"cos(x²)dydx O"…

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Q: +[2yln [2yin (3 3y²dx 3siny dy = 0 ;when x = 1, y = 0 5x x2+3x x+3,

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Q: O y²dx + Cory ty² -Ddy

A: Given y2dx+(3xy-y2-1)dy=0

Q: 2 2х-4 2у — 1 dydx x + 1 ) Q2. Evaluate the double integral

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Q: Integrate  zex^2 + y^2  over the cylinder  x2 + y2 ≤ 25, 2 ≤ z ≤ 5.

A: Integrate zex^2 + y^2 over the cylinder x2 + y2 ≤ 25, 2 ≤ z ≤ 5 as follows.Here, x2 + y2 = 25 and…

Q: Consider the vectors x1 (c) What conclusion can be drawn about the coefficients in the system of…

A: Given vector is, X1=t22tX2=etet Part(c): In case of linearly independent vectors X1 and X2. The co…

Q: х-11 b. S- dx x2+3х-4 2x-+х-4 dx| х3-х2-2х С.

A: Consider the integral  b)      ∫x−11x2+3x−4dx ∫x−11x2+3x−4dx=∫x−11x+4x−1dx Now use partial fraction…

Q: y" + 4y' + 3y = 0, y(0) = 2, y(0) = -1

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Q: To evaluate fx²cos x²cosx dx use integration by parts. What is the expression after the second…

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Q: find the integrating factor of (y² - x ) dx + 2ydy = 0

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Q: - Second order : non- homogeneous Equations with Constant Coefficients d²y 4-- + 16y = 10 cos 4x dx²

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Q: 4. x(x² – y² – x)dx – y(x² – y²)dy = 0, y(2) = 0

A: For the solution follow the next step.

Q: I. Integration by pa 1. Su²sin2u du 2. S y²e2ydy

A: The given integral is,1.∫u2sin2u du2.∫y2e2ydy

Q: An object of mass m falls from rest and its velocity v given by dv m+kv =S. dt Use the Integrating…

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Q: (x In 2x dx = u v- Jv du -Svdu- Using Integration By Parts, Fand uv- fvds uv- Jvau 3 3 xVX In 2x-V지…

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Q: Obtain the solution using Integrating Factors Found by Formulas. 1.) 2(2y² + 5xy - 2y + 4)dx + x(2x…

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Q: (1+x^3) dy-x^2ydx=0 satisfying the initial condition x=1, y=2

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Q: y" + 3y' = 0, y(0) = -2, y'(0) = 3

A: The solution is given as

Q: 1. y(x³ – y)dx – x(x³ + y)dy = 0

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Q: y= 0, y(1) = 1, y(1) = 0

A: We have to solve given problems

Q: 1 find the total differential dz. z=xsin y + x² z = (2x² + 3y)² z=5x-7y

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Q: 2. Reverse the order of integration of S Saz dxdy. y+2

A: The objective is to reverse the order of integration

Q: 6. Find S(3y – y³) (1– y?)dy sin ycos y 7. Integrate: J sin² y dy 8. Find 3 S(5 - 3y-5)²dy

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Q: 2) z³ - 3x ²y + 6 xyz = 0; use the method of partial differentiation Əz Əz to find 2x 1 ду

A: The given equation is z3-3x2y+6xyz=0. Find the differentiation ∂z∂x, ∂z∂y of the given equation.…

Q: 1 COS Z dz, C : |2| = 3z Integrate counterclockwise 9. COS Z dz 3z

A: We have to find Given Complex integral using Cauchy Residue Theorem.

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