Maximize f = 3x1 + 7x2 + 8x3 subject to 4x1 + 2x2 + 3x3 < 12 xi + 4x2 + 3x3 <24 T1 20, x2 > 0, r3 >0 If no solutions exist enter DNE in all answerboxes. T2 = I3 f = J00

Q: Obtain the general solution by separating variables. SHOW YOUR SOLUTIONS. xydx - (x + 2)dy = 0

A: Given problem:- Obtain the general solution by separating variables. SHOW YOUR SOLUTIONS.   xydx -…

Q: 13. y = x'/9, 0 sxs 2; x-axis

A: The formula for area of revolution of a curve on interval [a,b] about x-axis is given as…

Q: Solve using crama's rule: 2x - 2y + 3z = 13 5x - y + 4z = 11 x + 3y - z = -10

A: We solve the system using Cramer rules

Q: The cubic function y = ax3 + bx² + cx + d pass through (0, -6), (1, -2) and tangent to the line 3x –…

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Q: 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.

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Q: y" + y = 2x

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Q: Obtain the general solution valid near the origin: x(x − 2)y" + 2(x − 1)y' − 2y = 0

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Q: Solve Ytt = = 4yxx 0 0 Yx(0, t) = 0, Yx(1, t) = 0, Y (x, 0) = 0, y(x, 0) = 3cos(2nx)

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Q: 2 √2x-x² SJ J² J²^ √√√x² + y² + 2 00 y²)[2x − (x² + y²)]dydx -

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Q: particular

A: We find particular solution.

Q: dy 8. V1+ V1+x 1

A: From the given problem: I=∫-18dx1+1+x   ...1 Let, u=1+xSo,dudx=ddx1+xdudx=0+1du=dxFor the…

Q: Solve by Graphical Method Max z=2x+4y Subjected to 3x+4y0

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

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Q: x+ y+ 2z=9 2x +4y - 3z = 1 3x +6y-5z 0 [1 1 29 2 4-3 1 3 6 -5 0 to the cecond to obtain

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Q: (ost) X= 3サ-3 DiD X-2-2y ¥ーにh で3,0) D3 Dy メーと2 サ=スメート X-4 <-リ-3 toノー4)

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Q: Solve 2sinx- V3 = 0 on interval [0,2 t)

A: We have to solve  2sinx - √3 = 0 on interval [0 , 2π)  Since ,  2sinx - √3 = 0  2sinx = √3

Q: Q5) by using the (graphical method) find the optimum solution of X1, X2 that the maximum Z=4X1+5X2…

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

A: Auxiliary equation for the given equation:

Q: y" - 5y' = x - 2, when x = 0, y = 0, y' = 2

A: We have to solve the given differential equation.

Q: Solve (D2 – 2)y =0 O a. y = cqevZx + c2e¬vZx O b.y= "(c,cos/2x+ c,sin/2x) O c.y = cqevZx+czxe¬VZx O…

A: The equation D2-2y=0 represent y''-2y=0 . Consider the solution of the differential equation is in…

Q: Find general solution of y" – 2y' + y = , By Variation of t2+1' parameter method.

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Q: Q3\ Solve the problem minimize * J[y]= [[v +y"- 2y dx ,subject to the conditions y (0) =1 and y(1) =…

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Q: Find the solution (varition of parameter)   X2y11-2xy1+2y=x3sin x

A: According to the given information, it is required to find the solution of the given differential…

Q: A Q2 Show that y=x+ is the solution of 3x – x = x+ y. dy dx

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Q: 3. 2y" + у' - 3 А. 3 В. Зх C. 3x D. x?

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Q: SOWE FOR THE ORTHO GON AL TRAJECTORIES y² = 4x² (1-ex)

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Q: Solve for A y and dy if y = f (x) = -3x + 2x2 – 3x +5 %3D and

A: Given that: y=f(x)  =-3x3+2x2-3x+5

Q: H4. Use the method of variation of parameters to find the general solution of dy -X- - 3y= 4x³. dr2

A: Please find attachment for the details solution

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

A: Solve the given problem.

Q: The monthly total cost function for a product is C(X) = 500x + 0.1x + 17,590 dollars, and the…

A: 1.)C(x) =500x+0.1x2+17590R(x) =1000x-0.01x2Break even point⇒ C(x) =R(x)Units = 35 , 4510

Q: 4. Find dyax and d2 x =V4- t , go t²-2t ye t'-2 get'.

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Q: Use the separation of variables method to solve 4UTr H Utt: 00 uz (0, t) = uz (2, t) = 0 u(x,0) = x,…

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Q: (T^2-x)dt-tdx =0 when t=1 x=5 Ans,: x=1/3t^2 + 14/3t please show solution

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Q: 3. Solve xy" + y = 0 given that y(1) = 1, y(2) = 2 taking h = 0.25 using finite difference method.

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Q: 2 ydx = 3xdy; when x = -2, y = 1 Ans. y = (x/2)3

A: Given: 2ydx=3xdy ; x=-2, y=1   We know that; ∫1ax+bdx=1alnax+b+C

Q: 2. Solve for y only using Cramer’s rule if: x + y + 2z = 3 2x − 3y +z = 0 3x + 3y +z = 5.

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Q: 8. Obtain the particular Solution by satisfying the conditions indicated. y' = x exp (y - x²); when…

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Q: 2. x (х — 2)у" + 2(х — 1)у' — 2у %3D 0 |

A: Power series solution of the differential equation

Q: Solve by making the appropriate substitution

A: Given equation

Q: general

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Q: Solve: sec x = V2 + 2πkk e Z U + 2π시k E Z 3. + 2πkke z 2Tk k EZ 4. 4 + 2rk|k € Z 3 + 2rk|k E Z 3. of…

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Q: Solve the non-homogeneous DE. Hint: Use method of undetermined coefficients. y(4) – y = 5; y(0) =…

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

A: Given: The given differential equation is y''-2y'+2y=1x, y4=0,y'4=0

Q: Suppose that 3x² - y² = t² and y=tsin 0. Find dy ().-0 (27). and X

A: Given 3x2-y2=t2 and y=tsinθ

Q: Evaluate the following integrals

A: The given integrals are,

Q: 2. Obtain the particular solution. y"-y'-6y=0; when x=0, y=2,y'=1

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Q: dz az %3D Jsing separation of variables method, solve "+ = (x+ y)z ду

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Q: f(x) = 2x5 + 15x4 - 3x3-4x2+ 7x+ 14 1)Trapeaoidal rule 2) Trape20idal rule with n=2 3) 1/3 Simpson…

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Q: 9. Find a quadratic function y = ao + a1x + a2x² satisfying y(1) = 1, y(-1) = 2, and y'(1) = 2.

A: put values and make equations then solve