Find the orthogonal trajectories of the family of curves. (Use C for any needed constant.) x2 + 2y2 = 16k2

Q: 3x* – 4y* = C

A: The given equation is: 3x4-4y4=c

Q: : Find the orthogonal trajectories of the family of curves y4 = kx³. (A) 2y³ + 3x² = C (B) 2y³ + 2x²…

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Q: determine the equation of the orthogonal trajectories of the following families curves: The…

A: Given that: y2=x3a-x

Q: : Find the orthogonal trajectories of the family of curves y4 = kx³. (A) 2y³ + 3x² = C (F) 2y³ + x³…

A: Introduction: An orthogonal trajectory of the family is any curve that cuts each member of a…

Q: : Find the orthogonal trajectories of the family of curves y4 = kx³. (A) ³ + 3x² = C (B) 2y³ + 2x² =…

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Q: Determine the orthogonal trajectories y-3x+1=ce 3x

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Q: 1) 3 Find the orthogonal trajectories of the family of curves y = 2x+k

A: Please see the explanation below

Q: Find the orthogonal trajectories of the family of curves. Use a graphing device to draw several…

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

A: y''-2y'+y=14x32ex find the roots for the homogeneous system  r2-2r+1=0 r-12=0 r-1=0 r=1 for one real…

Q: (6)Find the orthogonal trajectories for the given families of curves 2x2 – 3y = K. Where K is a…

A: We have to find out the orthogonal families of given function Given function   2x2 -3y=K  ;    where…

Q: For the family x² + 3y² = c, find that member of the orthogonal trajectories which passes through…

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Q: Which of the following is the orthogonal trajectories of the family of curves y^(5) = kx^(4)? There…

A: To find orthogonal trajectories in the curve substitute -dx/dy for dy/dx in the differential…

Q: find the orthogonal trajection of the family of curves x2+y2=a2

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Q: Use the explicit Euler method to plot the  estimate y(2) if y(t) is the solution to y' = t - y3 with…

A: Given IVP is y'=t-y3, y(0)=1 we have  f(t,y)=t-y3 Here using n=10 steps, Then step size h=upper…

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: 2. Find the family of orthogonal trajectories of the given family of curves in the following…

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Q: Find the orthogonal trajectories of the family of curves x² - y² = (² A x² + y²=C² B) xy=C (C) x-y=C…

A: We can solve as follows

Q: The orthogonal trajectories of the family of curves y= cx2 is A x=ky? B x? +2y? =k © x2 = ky? D…

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Q: The orthogonal trajectories of the family of curves y = cx2 is A x=ky? B x²=ky² © 2x2+y²=k D…

A: Solution

Q: PART B: Find the Orthogonal Trajectories of the given family of curves. 8. y = c²(x² + 4y²);

A: Given curve is: y4=c2x2+4y2 To find the orthogonal trajectories of the given family of curves. From…

Q: Find the orthogonal trajectories of the family of curves x²- y2=C² A) x- y=C (B xy3=C xy=C D…

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

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Q: The orthogonal trajectories of the family of curves y= cx2 is A 2x²+y²=k B x²+2y²=k © x=ky? D x²=ky²

A: Given family of curves is y = cx2 We have to find the orthogonal trajectories.

Q: 7

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Q: (6) Find the orthogonal trajectories of the family of curves y = ax? + 4ax + 4a, where a being…

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Q: A parabola has the equation y^2 = -4ax. Determine the slope of the orthogonal trajectories. 2x/y O…

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Q: The orthogonal trajectories of the family of curves y= cx² is A x=ky? B 2x2+y2 = k © x2 = ky? x2…

A: The given family of curve y=cx2

Q: Give the family of orthogonal trajectories for the equation: y2 = Cx5+5

A: To obtain the family of orthogonal trajectories for the equation: y2 = Cx5+5. Find a differential…

Q: The orthogonal trajectories of the family of curves r = f(0) is solve by using the following…

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Q: Find the orthogonal trajectories of the family of curves y = kx'. = C (C) 3 y³ +x? = C (D) 3 y³ + 3…

A: Given y5=kx5 To find the orthogonal trajectory

Q: Find the orthogonal trajection of the family of curves x2+y2=a2

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Q: Q.NO.2: a) Find the equation of the orthogonal trajectories of the family of curves. x²y² = 4c²

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Q: The orthogonal trajectories of y 4az is , where a is arbitrary constant O + = 2c %3D = 4c 2 O y+a -…

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Q: determine the equation of the orthogonal trajectories of the following families curves:…

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Q: : Find the orthogonal trajectories of the family of curves y4 = kx³. (A) 2y³ + 3x² = C (B) 2y³ + 2x²…

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Q: Find the orthogonal trajectories of the family of curves y = ce^x. Select the correct response: x^2…

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Q: Find the orthogonal trajectories of the family of curves y^3 = 3(x-c). Draw a few representative…

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Q: Find the Orthogonal Trajectories: a.) y6 = C (x2 + 1)

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Q: The orthogonal trajectories of y = ce5" where c is arbitrary constant. is - 2x + 2C = 5y? 2x + 2C =…

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Q: 4) Find the orthogonal trajectories of the family of parabolas y – 3 = c(x + 1)².

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Q: y = 3x - 1 + Ce-3x Find the orthagonal trajectories to the given curve.

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Q: Find the orthogonal trajectories of curves represented by x = Cev Select the correct response: y =…

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Q: Find the orthogonal trajectories of a system. x'y2- 2xya + a2 0 %3D

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Q: find orthogonal trajectories of   x2+(y-c)2=c2.

A: x2+(y-c)2=c2 now differentiating both side with respect x , we get 2x+2(y-c)dydx=0 or, dydx= -x(y-c)…

Q: The orthogonal trajectories of the family of curves y= cx² is A x² = ky? x² +2y² =k В © x=ky? D 2x2+…

A: In this question we have to find the orthogonal trajectories of the family of the curves y=cx2

Q: Find the family of orthogonal trajectories of the given family of curves in the following equation…

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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.