16) If x = 5y and y -2a, express x in terms of a. %3D 18) Which expression is equivalent to (9x y° (1) (2)3xy³ (3)-

Q: 3. (x² + 6y²)dx – 4xydy = 0 , y(2) = 1

A: Problem is in the form of homogeneous form...so put y=v.x and proceed as I have done solution step…

Q: 4x Compute (2x + 4yz) dz dæ dy 1

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Q: Find the particular solution of 9. 12+ 4y = 3x – 1 given that when x=0, y=0 and dx

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Q: O': what is the general solution of the equation. dy dr xy

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Q: 4. Find an implicit solution using the substitution u= or y3ux dy dx x+xy %3D

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Q: 1 By using completing the square , dx can be rewritten as /x²-4x – 7 1 VTr- 2)²– 3 1 =dx V(r- 2)? +3…

A: We need to write the following integral by completing the square   ∫1x2-4x-7dx

Q: When reduced to a linear DE of order one in z, the Bernoulli's equation +y()= 3x?y² becomes +z(-÷) =…

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Q: Consider the following IVP: y"- y = 4cos t; y(0) = 0, y'(0) = 1   Find the general solution.

A: The given differential equation is: y''-y=4cost So, we can also write as: D2-1y=4cost So, the…

Q: 1.Solve the given problem W = f(x, y, z) = 3x²y+ yz² + 2z³ fxis equal to ? fyis equal to ? fzis…

A: Follow next step

Q: Show that the equation dy + 2k possesses solutions of the form Σ 2 c, e cos (a, x+ E,) cos (w,t +…

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Q: (2) Find the value of m so that y = emz is a solution for z'y"-y = 0.

A: Given that the differential equation x2y" - y = 0 has a solution of y = emx To find out the  value…

Q: Let z=xIn(x²+y²-e)-235xy, x=te, y=est. If the value of oz when s=2 and t=1 is equal to Ae?+Be", then…

A: Here, the given functions are: z=x lnx2+y2-e4-235xy, x=t es, y=est so, z is a function of x and y…

Q: 2. Given that y = (a + bx)e-* where a and b are constants, show that +2 +y = 0 dx2 dx

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Q: Given y = Vx – 2Va – 2; Find y'. - |

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Q: The approximation of I = (x-3)e* dx by composite Trapezoidal rule with %3D n=4 is:

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Q: fin the general solution of (x+2y-4)dx - (2x+5-y)dy=0

A: Please see the below picture for detailed solution.

Q: 3. Is y(x) = C,sin2x + C2cos2x, where C1 and C2are arbitrary constants, a solution of y" + 4y = 0?

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Q: 41n <ys 28 31r x = sec* (7t) – 1dt, | 21 41x 28

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Q: дz For z = x² + xy³; x = uv² + w², y = u + vew, find when u = 2, v = 1, and w=0 dv

A: Let's solve given derivative functions.

Q: what is the privet solution to thhe equation (6+0)ycx)= Xsin cx) (X) %3D

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Q: 4. Give the graphical significance of the constant k for the equations of the form y=(x-h)³ +k

A: Given curve is y=(x-h)3+k

Q: (b) Use the substitution u = x In y to solve the equation (ry + 2ry In² y + y In y)dx + (2x² In y +…

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Q: What is the general solution to the following equation: (dx/dy)+ xtan(y)=2tan(y)

A: rewrite the given equation in the form of separable differential equation and integrate…

Q: 2 ydx + x(x In y – 1 )dy = 0 %3D

A: Given that: 2ydx+x(x2lny-1)dy=0

Q: Use Secant method to find to find solution accurate to within 10 for the following problem. (i).…

A: Given function is  (i) f(x)=3xex Here x0=1, x1=2 f(x0)=f(1)=3(1)e1&gt;0 f(x1)=f(2)=3(2)e2&gt;0 Since…

Q: 13. Differentiate y = e** with respect to x . ,3x+1 C (3x+1)e³x! D 3xe*+1 O A В D A

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Q: 1. Solve for the othogonal trasctories y =x²(1-cx)

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Q: The equation (3xcos (3a) + sin(3x)-3) dr + (2y + 5) dy = 0 is e rcos (3z)- 3 + y - 5y = C O zsin…

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Q: Use the method of variation of parameters to solve the following y + 4y + 4y e- In z, z>0

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Q: 3. Show that the equation (x²y)dx + () dy = 0 is exact and then solve it.

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Q: 4(a)Verify that the equation y = Inx – Iny is an implicit solution of the TVP, ydx = x(y+ 1)dy y(e)…

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Q: Given x²y3 = In(xy) Show (using complete solution) if the equality below holds dx (x\(3x²y3 – 1\ dy…

A: NOTE: Refresh your page if you can't see any equations. . take the derivative with respect to x

Q: 3. Find the general solutions of, dy _ x+ y dx х-у, a.

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Q: Q2/A/<he di fferential equation is yedx +3xay+dx +dyno diff erential when fineling the solution to a…

A: To find: The solution of differential equation y2dx+3x2y2dx+dy=0 and also find the constant (c) at a…

Q: dz 10. Compute az and for the following equation. dy e Y + xz? 6xy*z3

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Q: 5 solve the 1UP: y% 4y(2)+ 3y'= Y1)=e+ % ,uG) = et %

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Q: b) Find the general solution of (3sin y– 5x)dx+2x² cot ydy = 0

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Q: Find the general solution of the di f ferential equation *+ x .2 d²y + (x² – )y = 0.

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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: What is the value of the arbitrary constant of the given DE (3x + 2y + 7)dx + (2x – y)dy = 0 at…

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Q: Show that the equation + 2k dy =c². possesses solutions of the form 00 2 c, e " cos (a, x + &,) cos…

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Q: Show that the equation dy + 2k possesses solutions of the form 00 Σ C,e -kt cos (a, x + E) cos (w,t+…

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Q: dy dx + 3x²y = 6x²

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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: Show that the equation dy + 2k possesses solutions of the form 00 - kt E c,e cos (oa,x+ E,) cos (w,…

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Q: Find dy/dx in terms of x and y if ax^2-by^5=c^2. Assume that a,b, and c are all constants.

A: Given equation is-  ax^2- by^5= c^2

Q: Why is e^x selected as u and not e^2x (to get du /2 = e^x dx in the problem attached?

A: Consider the integral  ∫e2xe2x+3ex+2dx

Q: Use the method of Variation of Parameters to solve the following DE: у" — у %3D2х2 —х— 3.

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Q: dy Find dæ |(7,9)=(-1,-1) if e sin (x? – xy) = y² – 1.

A: Given,          xsinx2-xy=y2-1

Q: Solve the variational problem 8] +2y (x +y)] de = 0, given y (1) éy (2) 0. %3D

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