f (x) = x³ + 2x² + 6x e Z¡[x] g(x) = x* + 4x + 5x + 6 e Z¬[x] O x+ 4 O None O x +1 O 2r + 1 O x + 2

Q: Find e* + x-2 + C e* – 1+ C + C (1/2)x² e* – In |x| + C

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Q: 16 Therefore f(x) = = co + C1x + c2x²+.. , where %3D x2 + 2x – 3 Co = C¡ = C2 = C3 =

A: given a function : f(x)=16x2+2x-3 We need to obtain it in the form of : c0+c1 x+c2 x2 + ... where c0…

Q: Find a particular solution, y,(x), of y(ª – y" = 12e3 – 5x + 2. -

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Q: f (x+2) In (x+2) - 4 tc (x+2) Xt *+ 2

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Q: (B) Find the solution of f(z) = x'+6x'y+i 3x'y by using Cauchy-Riemann method

A: we have to solve the given problem

Q: Solve the nonhomogeneous ODE. y" - 6y' + 9y =x²e5x

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Q: Find the solution by using Solution of 2nd order D-Es 2 X ý XỨ ty - xy + y = Lnx -

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Q: x = c e + c2t e“ O x"- 36x'+ 12x 0 6. O x"- 12x' + 36x = 0 %3D O x"+ 12x'- 36x = 0 O x" - 4x'+ 9x =…

A: for a differential equation having repeated roots m of auxillary equation thenthe solution or the…

Q: a) 2xy dx+(1+x²)dy=0 b) y'+(4/x)y=x* ------by exact method ---by linear method

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Q: Obtain the general solution. xy3dx+ex^2dy=0

A: The given differential equation is xy3dx+ex2dy=0. We have to obtain a general solution.

Q: (e) x+ 2x + 3x, = 0 (f) x- 3x +2r, 2x)- x +x = 0 X- 2r2 + 2rs -2x1 +x2 = 0 0. 2x) + 3x + 4x, = 0 (g)…

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Q: What is the particular solution for y′=−2e^x−3x^2+x−4 such that y(0)=1?

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Q: (c) Show that V(3) = o²(X'V-¹X)-¹.

A: 3. c From the given information, y=Xβ+ε Eε=0, Vε=σ2V From the part b, β^=X'V-1X-1X'V-1y

Q: x'y" – 3xy' +4y=x° Inx

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Q: The solution of y2 – x²y' = 0 with IVP (1)= . is given by y(x) = 1+x 1 y(x) = 1+x 1 y(x) = 1+ x2 (x)…

A: Given initial value problem y2-x2y'=0    ; y(1)=12

Q: - 3)²y" (x) - 3(x-3)y'(x) + 3y(x) = 2(x-3)^e², x > 3. Verify that y₁(x) = (x-3)³ is a particular…

A: Given the differential equation: x-32y''x-3x-3y'x+3yx=2x-34ex To find the solution of above…

Q: (a) f(x) = (2x – 1)*(3x – 2)³ (b) f(x) = [(x – 3)(5x + 1)]³ (c) f(x) = Vx cos ((3x + 2)²) %3D CoS…

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Q: der the problem maxx + 2y subject to x² + y² ≤ 1 and x + y 20

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Q: Given that y,(x) = e²^ is a solution of y" - y' - 2y = 0, use the 2x Reduction of Order formula to…

A:

Q: Q1: Find the general solution of the y - 4y - 5y = 2sin2 x

A: Given differential equation is y''−4y'−5y=2sin2x. We have to find the general solution of the given…

Q: y''-4y'+4y=0      y1=e2x   using reduction of order

A: y" - 4y' + 4y = 01 — (i)Given y1 = e2xLet y = y1v = e2xv       y' = 2e2xv + e2xv'      y" = 4e2xv +…

Q: r²[(x²-y²)²] 1²₂5²² du dt x+y

A:

Q: Q2\A: By using partial method solve 2x² cos x dx

A: Given :∫2x3cosxdx

Q: X - X (x -x* Y (r-F)} (x-X{r-F) Y-F 2 4 3 6. 6. Compute: X = Y = E(X-XXY-Y)- N-1 B A = Y - B*X = 2.…

A: The table is given as follows x (x-xbar) (x-xbar)^2 y (y-ybar) (y-ybar)^2 (x-xbar)*(y-ybar) 0…

Q: a) z=-x² + y² c) z² = x² + 2y² e) x² + y²-z² = 1 b) z=-x²-2y² d) -x² - y² + z² = 1

A: match the following quadratic surfaces with the following equations (a) z=-x2+y2

Q: Find the General and Particular solution of = 3y ; y = 3, when x = 0

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Q: the differential equati x²y' – 2y = Inx² is cje2* + c2e¯* – x + 5 O c1x² + c2x=1 – In x + ; O 2 +…

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Q: Find the particular solution of y' = x^3 - 2xy when x = 1, = 1. O 2y = (x + 3)^0.5 In(2x+3) O 2y =…

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Q: Given that y1 = 3x is a solution of æ°y" + xy' - y = x2 on the interval (0, 0), use the reduction of…

A: Concept - used the reduction of order

Q: Find the solution. xy'+ xy = 1 - y, y(1) = 0 A y = x-'(1 – e!-") y = x-2(1 + e'+*) © x=y-'(1 + e'-1)…

A: Given differential equation is xy'+xy = 1-y, y(1) = 0

Q: O': Find the general yy' – 2y² = e²

A: A first order Bernoulli ordinary differential equation is of the form dydx+pxy=qxyn Where p(x) and…

Q: Find the su x² + y? :

A: The surface is given as z=xy. Take the derivative of the surface, z=xyfx=y, fy=x. The surface area…

Q: Solve the equation using Reduction of Order y" -y = 2et Oy=c₁e¹ + c₂xet + e* (x + c3e-²x + C4)…

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Q: Determine the general solution of y" - y = 0 given y₁(x) = e-2x using reduction of order

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Q: z x ² dy 2X ax x² + y² X

A: To evaluate the given differential equation.

Q: = (y² – z² +3yz – 2x of the following is/a

A:

Q: Verify that y = c1x+c2Vx+ is the general solution of the 6x following nonhomogeneous 2.²y" – xy' + y…

A: Derivative of xn: Derivative of an exponential function that is, xn is given by the formula,…

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: (b) Solve y" + y = 0, y(0) = 3, y(1) = -3 by using finite-difference method with h = 0.2.

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Q: Show whether the two equations y₁ = using the Wronskian. 12e and y2 1.2e are independent or…

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Q: Evaluate /, a Te dydx y2 2 JJ4X-x² 32 dydx (x²+y²)' V4x-x? O 4 In(v2 – 1) – 4+7y/2 3 4 In(v2 + 1) –…

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Q: X+x- L-X+, dt 2 x²-1

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Q: 1+x² »" – 2xy' + 2 y = 0 y (x)=x

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Q: Find the general solution of xy²y' = x²y-y³. x2 y² = (C+ 2ln(x)) Oa. O b. 2x2 (C+2ln(x)) Oc2=x²+ x2…

A: We need to find the general solution of given differential equations.

Q: I need help checking my answers. Thank you for your help.

A:

Q: determine the general solution of y''-y=0 given y1(x)=e-2x using reduction of orders

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Q: 4. Are y1 (x) = e*and y2(x) = x + 1 solutions of the D.E. xy" – (x + 1)y' +y = x2. Are y1(x)…

A:

Q: 1 Find the general solution of x'y" +xy' -y= x+1

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Q: f(x) = é ーx46x? J6-6x -6 A) e-+6z² (-6x³ + 12x) + 2/6 – 6x Calculate f (x) 1 2/6 – 6x B) e-+6z°…

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Q: 2. Solve for x O (x – 4)(x + 7) =0 d) x - 12 = 37 g) x = 10x b) 2x(x + 8) = 0 e 9x = 25 c) x = 4 4x…

A: To determine:Solution of the following equations 1. 4x2=4 2. x2-4=32

Equations and Inequations

Equations and inequalities describe the relationship between two mathematical expressions.

Linear Functions

A linear function can just be a constant, or it can be the constant multiplied with the variable like x or y. If the variables are of the form, x2, x1/2 or y2 it is not linear. The exponent over the variables should always be 1.