3) Prove thet the xy-plane with constant curva tue k= urve In is o circle of radious

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Q: HW8 : Topic differential equations 6.)

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Q: (x+y)dx + Jx? + y2 dy is an example of homogeneous functic OTRUE O FALSE

A: To determine whether the below differential equation is homogenous or not. x+ydx+x2+y2dy

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A: As per the question we are given a set of four independent variables with observations.Now we have…

Q: (D* – 1) y = 0 O y = cje* + cze* + c3 cos x + c4 sin x O y = cje* + czxe* + C3x? cosx + C4x³ sin x

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Q: What is the Laplace Transform of e^3t?

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Q: OUESTION 2 Show That yi= dx ta ĝ yo =-x° are both soluhions of y= xy'+ (y)? Are the c wn stant…

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Q: Differential Equations First Order Linear Differential Equations (v - cos ?x)dx + cos x dy = 0 %3D

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Q: Find the slope of the curve x? – 3xy + y² – 4x + 2y + 1 = 0 at the point (1, -1). с. 1/3 d. 1/5 а.…

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Q: Solve the iべtial value probdem usine Laplace transformotion y (H) + 2y' (+) +5y(+) = esint y lo)-0

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Q: the plane according to the equations x = t² + 2t and y = 2t³ – 6t. Find dy/dx c. 3 d. 4

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Q: RFind the Jeneral Solution of -2. 6.

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Q: What is the Laplace Transform of t^4?

A: we have to find laplace transform of t4

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Q: 4. Find the orthogonal trajectories of the family of curves: y = ke* %3D

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Q: 1. Tell whether t² et is a) piece-wise continuous for t≥0 and b) of exponential order for t≥0.

A: (.)  Given function is ,                     (.) Piecewise continuous function:   The function is a…

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Q: defirntion. yc fucon hg Suon ha hnd fhe Laplace Transfurm

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Q: Consider the differential equation 2²y" – x(x + 2)y + (x + 2)y = 0, x > 0 - 3.

A: Given: x2y''-xx+2y'+x+2y=0, x>0   To find: A second solution y2x using the solution y1x To show:…