Solve the problem. Find C(x) if C'(x) = 5x 2 - 7x + 4 and C(6) = 260. 7 A C(x) = x 3. x 2 + 4x - 260 3 B C(x) = x2 + 4x + 2 2 7 C(x) = x2 + 4x + 260 2 7 D C(x) = 을 x3- 극 x2 + 4x - 2

Q: 9. Solve d²x dt² + 4x + 5y = 1²; d²y dt² + 5x + 4y = t +1.

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Q: Ⓒ Solve зик subject to + 2x x = 0 u(x,0) = in Rx [0,00) n(x)

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Q: Find the general solution of the DE (2y – x2) dx + (y+2x) dx=0 А) 2ху + 3 y2 =C 2 (в) 2ху — 3 x3 y2…

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Q: 1.What is the third derivative of y = 2x5 – 2x4 + 5x3 + 6? 2x – 2x + 5x? 40a O A. " = - O B. " 24x +…

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Q: Solve fractional equation. スx いlo 2x+5 4x+10 2x 11 2xf5 4Xナ10 スx スx+5 スx ef ス×+5 スr+5 why does…

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Q: 4. Solve the particular solution of y" + 3y' + 2y = 6e¬, y(0) = 1, y'(0) = 2, using a. Variation of…

A: we have given the differential equation y"+3y'+2y=6e-ty(0) = 1, y'(0) =2 we have to find the…

Q: ) Obtain the general solution of y" + 2y + y = e² In r

A: In this question, the concept of the differential equation is applied. Differential Equation A…

Q: find general solution. dr/dt= -2tr,         r(0)=ro

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Q: dy = -8xy² dx 3. Solve + 4x(4x+1) y-(8.x² +4x² -1) by knowing u =x is a solution.

A: Given: dydx=-8xy2+4x4x+1y-8x3+4x2-1

Q: ye2xdx ye2x. (4 + e2x)dy

A: The given equation is ye2xdx=4+e2xdy The given differential equation can be solved by converting it…

Q: A. ELIMINATE THE ARBITRARY CONSTANT/S IN THE EQUATION. 1. y= Ae2x + Bxe2x 2. y = Ax² + Be¬* 3. y =…

A: Explanation of the answer is as follows

Q: Solve a & b with given A[r = 3x şax+ (y + z + 3) Ay +(6x - z³) a₂] where: np = ax + 4ay - 2az 2+y³

A: Given

Q: (x) + Find the general solution аху- х+у о у-xlncxЈtc 2 x² Ў= х²-хутуг у-х- х Нихте з y = x + y + y…

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Q: Find the general solution of using the method of variation of parameters. d²y dy 2- - 42+ 2y = xe 2x…

A: Given,2y"-4y'+2y=xe2xComplementary SolutionAuxiliary Equation is 2m2-4m+2=0⇒m2-2m+1=0⇒m-12=0⇒m= 1 ,…

Q: Find the general solution using variation of parameters. y" – 4y + 4y = (x + 1)e²"

A: Given differential equation is, y"-4y'+4y=x+1e2x The auxiliary equation is, m2-4m+4=0m-22=0m=2,2…

Q: - r)rdrde 32(V2-1) 16(VZ-1) c. VZ-1) 4(VE-1), S(V2-1) a. d. 3. 3 3 e. 3.

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Q: Suppose ay″+by′+cy=0 with y(0)=d and y′(0)=k has a general solution y=5e^(3x)−xe^(3x).   What are…

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Q: dy Solve of y = e2-3+18 In(e2²-30+18 da A. y' e2z²-32+18 (8x3 – 18z² + 85x – 57) B. y' e2a2-3a+18…

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Q: Find the general solution of (xy² + x²)dy + a. 3xy + y3 = C b. 3xy - y3 = C xydx = 0 с. -Зху - уз с…

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Q: 10--6A Oa) x- -6 V b) x = 6 c)x- 10 V d) x- -2 Oe) x- -8

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Q: value of c in the equation: dV/dt = -500 (t+1)-2, when  V=700and t=0 is

A: follow next step

Q: Use variation of parameters to find a particular solution of 14aie" 3 y" – 2y' + y - Yp(x)

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Q: how would I take the partial derrivitive of this equation, I cannot use the chain Rule as we have…

A: Given function,

Q: 10. Find the particular solution that satisfies the initial condition. my'+2y = 3x2-5x, Initial…

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Q: Solve: y" + 4y" + 29y' = 0 O y = C1 + C2e5ª cos2x + C3e5" sin2x -2а O y = C1 + C2e¬2ª cos5x + C3e¬2®…

A: The given equation is y'''+4y''+29y'=0 First write the auxiliary equation and then solve it to…

Q: 2. (D² - 3D + 2)y=1+x

A: The given differential equation is;  (D2-3D+2)y=1/(1+e-x).

Q: What is the general solution of xy(xy5 −1)dx + x²(1 + xy5) dy=0 ? A 2x³y³-3x²= Cx² B 2x³y5-3x²=Cy²…

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Q: 4 Solve y" – y" – y' + y = 2e¬t + te' + 3 by using both the method of undetermined coefficients and…

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Q: 1. Eliminate the arbitrary constants in the equation given by: (x- a)(y – b) = 1 |

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Q: How would you interpret the coefficient of β2 in each model? Ln(Y) = β0 + β1 Ln(X1) + β2 Ln(X2) +…

A: Note : Since we only answer up to 3 sub-parts, we’ll answer the first 3. Please resubmit the…

Q: Find the solution. y' = 5y + e-2x y-2, y(0) = 2 -15x 13e A) y = + 3e 2r1/3 23 139e 15x – 3e -2x \1/3…

A: Given differential equation is in the form of Bernoulli's differential equation.

Q: Solve the particular solution (D2 + 3D + 5)y = 5e-x sin (2x) using D - operator method.

A: We find the particular solution of  (D2 + 3D + 5)y = 5e-x sin (2x) using D - operator method.

Q: Assume that a factory can produce a quantity 2x3 + x°y + y4 of goods, when x is skilled workers, and…

A: Here we use the concept of implicit differentiation.

Q: Solve for the general solution * (4xy+3y – x) dx + x (x + 2y) dy = 0 x' (4xy² + 4y – x) = c x²…

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Q: b) Give a particular solution for y" – 2y' + y = et - 1+x2

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Q: To find the daily optimum production number of Portland cement in a factory, one needs to solve the…

A: Given system of linear equation is 10x1-x2+2x3=6-x1+11x2-x3+3x4=252x1-x2+10x3-x4=-113x2-x3+8x4=15 To…

Q: What is the solution of (2x - y)dx + (4x + y– 6) dy = 0? а. (x+у-3)°- с (2х +у- 4)? b. (x-y+3)²=…

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Q: Solve for the general solution xydx - (x² +2y² ) dy = 0 x² = 4y° In(2 ) xy = 4y° In() Option 1…

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Q: 5. Use variation of parameters method to solve а. a. y" – 2y' + y = 1+x2

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Q: 20. What is the solution of (2x - y)dx + (4x + y – 6) dy = 0? a. (x+y- 3)° = c(2x + y – 4)² b.…

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Q: Solve by making the appropriate substitution

A: Given equation

Q: What is the particular solution of 2xyy' = 1+y2 , when x =2, y = 3

A: The given differential equation is solved below in detail.

Q: 8) Use Gaussian Elimination to solve: x +3y-z = 13 - 5z = 23 (4x-y-2z = 14 Consier 2x

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Q: What is the general solution of xy(xy³ −1)dx + x²(1+xy5)dy=0? (A) 2x5y³-3x²= Cx² B 2x³y5-3x2= Cy²…

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Q: 4. Solve y"- 4y' +3y = 1 by variation of parameters. %3D 1+e-*

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Q: /25-22-y2 zVx² + y? + z² dz dy dr

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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

Q: What is L[y] if y = u3(t) (t- 3)2? %3D L[y] = e3s . - 3 O Lly) = e3s. 2 L[y] = e-3s. 2 O Lly] = e-3s…

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Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.