To the reci max z Ax1 +B x2 A=6 s.t. 2x +4x 2 12, B=1 -X1 + 2x2 S 2, X1 20, x2 Free.

Q: Evaluate the integral (2 + 6) (2? + 6z + 2)*dz by making the substitution u = x² + 6x + 2. + C

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Q: 2) vting daplace toansfóöre, Solve x" Zt)+4x'Lt)+3=(4) uing = 10 gint yeren that xco) = -3t Ans: ILt…

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Q: 8x²y" + 10xy' – (1+ x)y = 0

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Q: 1. Using the first prine =) , show that (1 – x*) + 4nxy = 0. %3D 2. If y = 1+x2, + qx2+rx +s passes…

A: Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: Find positive numbers x and y satisfying the equation xy=20 such that the sum 4x+y is as small as…

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Q: Use variation of parameters to find a general solution: y(3) – 4y = et.

A: Given differential equation: y3-4y'=et         ...(1)

Q: Find the Solution (1+12) ds + 2t[st² – 3(1+12) 2]dt = 0; when t = 0, s = 2. %3D

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Q: (r+6)dr 4. S (z+2)?

A: Given: = The indefinite integral is, ∫(x+6)(x+2)2dx To find: -The complete solution of the given…

Q: Find the complete solution of the given DE using the Method of Variation of Parameters: y" + 4y asC…

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Q: Solve for z if cosh z = V3i.

A: Simply put cosh z= 1/2(e^z+e^-z)  Then simplify  then finally got quadratic in e^z  then find the…

Q: Proivde general solution of the given ay'' + by' + cy = 0 and b^2 - 4ac > 0

A: ay'' + by' + cy = 0 and b2 - 4ac > 0 We need to provide the general solution of the given…

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: 8. Find the partic ular solution of x²y" + xy' = 1; y = 0 and y' = 1/2, when x = 1.

A: We have to find the particular solution of x2y''+xy'=1 ; y=0 and y'=12 when x=1.

Q: Determine the interval of validity for the solution of the following IVP without solving it. (t2…

A: Given: t2-9y'+2y=ln20-4t, y4=-3 To Determine: Determine the interval of validity for the solutions…

Q: determine the second approximation Xz if Ne wtons Method was use to defermine the root o f the…

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Q: Prove that in the pairs of positive numbers ¤, y for æ² + y° = r the sum a+y is greatest when z = y.…

A: Here we solve the given problem of calculus.

Q: Find the general solution by using reduction of order method to (x2 + 1)y" – 2xy' + 2y = 0 given…

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Q: Use the modified Euler method of Lecture 3, with n 10, to find xt1 = -t, (0) = 0

A: Consider the given differential equation.

Q: Q3. Verify that y² = x² – 3 is the particular solution to the following ivp: y' = ; y(2) = -1. %3D

A: To check whether a solution is particular solution to ivp , it must satisfy the differential…

Q: y" -4y' + 13y :

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Q: m21 is nine times as large as m z2. Find mz1. -1 is supplementary to 2.

A: m∠1=9  m∠2                                       ------(1) and  m∠1+ m∠2=180°…

Q: Q(2): Find the general solution of x³y" – 3x²y" + 6ry' – by = xª In x. %3D

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Q: 4. Find for the particular solution of y' = x3 – 2xy when x = 1, y = 2 %3D

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Q: Find the general solution to the DE using the method of Variation of Parameters 8 y" – 4y = e2x + 1

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Q: Find positive numbers x and y satisfying the equation xy=24 such that the sum 4x+y is as small as…

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Q: Use Variation of Parameters to obtain the General Solution 1. y +4y 4-sx2x

A: Solve the given problem.

Q: Suppose that x-y" + axy' + by = 0 has the general solution of the following form: y = C,x³ + C2x³ In…

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Q: 4. Solve the IVP: d?s t3, dt2 A. 20s = t5 + 200t – 100 B. 20s = t5 – 200t + 100 s(0) = 5,s'(0) = 10…

A: Given IVPd2sdt2=t3, s0=5, s'0=10sinced2sdt2=t3on integrating

Q: Find solution n f(x) 300 2.4771 x (301) using newton backward 304 2.4829 305 2.4843 interpolation…

A: Introduction: Interpolating polynomial is the polynomial having the least possible degree that…

Q: dr a) de rcose + rsene subject to r(0) = 1 (solve by separation of variables)

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Q: V Solve usinog variaton of parameters or reduction of order (D²- 2D+1) y = e2"(e*+1)?

A: Solve by using variation of parameter  find auxiliary equation and then find wronskian and put in…

Q: 5. Find the second solution by reduction of order method: (1- 2x? y" + 4xy' – 4y=0 y, (x)=-2x

A: Differential equation and it's solution

Q: Ex:- Min Z= X-3 X2-2 X3 %3D sub to 3X1 - X2 + 2 X3<7 -2 X + 4X2 く12 -4Xi+ 3X2+8X3 slo Find anew…

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Q: use Lagrange method fixi O 3.7 O 1.3 2 2.5 4.8 - Nm su 6 7 t's 6.2 8.0 9.7 तज् 7.8 3.3 9.2 ㅋ.ㅋ 6.0

A: Solution: From the given information,

Q: Solve for z if cosh z = v3i.

A: Given cosh z=3ι. Expand cosh z to solve for z.             ez+e-z2=3ι              ez+e-z=23ι…

Q: it as a Bernoulm cquaion in the uependeht varlavic A. 0. 2x'y = y(y? + 3x). Solve by two methods.…

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Q: 6y" – 7y' – 5y = 2x³ + e¯* – 5 -

A: Ordinary differential equation involves the derivative of single dependent and single independent…

Q: Use the IVT to prove thatx^2+ lnx =1/2 has a solution.

A: Use the IVT to prove thatx^2+ lnx =1/2 has a solution.

Q: (D* – 4D³ +14D² – 20D +9)y = 0 - -

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Q: 2. Find te gunural soiUtion of 2

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Q: Also p; 2 0 for all j = {1, ., k} and E-1P; = 1. What is the value of E(X) and V(X)?

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Q: Solve by making the appropriate substitution

A: Given equation

Q: In a simple electric circuit, Ohm's law states that V=IRV=IR, where V is the voltage in volts, I is…

A: Application of derivatives

Q: Find the general solution to the DE using the method of Variation of Parameters 8 у" — 4у 3D e 2x +…

A: Introduction: The formula of the particular solution by the variation of the parameter of the…

Q: The solution of the IVP t(t + 4)y + (t + 4) y =t, y(2) = 2 exists in the interv

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Q: Is a solution of the diffrntish epuation 1 yy'= -X+ with y E € ]_9,GE with x € C-G,G] 2. 3)yy:…

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Q: Find the first approximation to the root of the equation x - 2x- 5 = 0using Regular-Falsi method…

A: Intermediate value property: Let f(x) be continuous function in a,band if f(a)&gt;0, f(b)&lt;0 then…

Q: Find the first approximation to the root of the equation x - 2x - 5 = 0 using Regular-Falsi method…

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Q: Verify that y = ODE y" + 3y' + 2y = 4x². -4e-x-2e-2x + 2x² - 6x +7 is a solution of the SHOW ALL…

A: We have to verify that y=-4e-x-2e-2x+2x2-6x+7 is a solution of the ordinary differential equation…

Q: 3a Show that the method xn+1 = Xn 6+ Xn ,converage to vā. %3D a

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