Find the general solution to a?y" + 5xy' - 2y = 0. OA. y = cje 4x + cze OB. y = c1x4 + c2x1 OC. y = ca(-2-V6) + cza(-2-võ) In]æ| %3D OD. y = ca(-2-võ) ) + cza(-2+v6) + c2r(-2+v6) %3D

Q: 1. Consider the differential equation (which we saw on the wk 1 test) dy %3D У (у + 1)?(2 —у) dt…

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Q: Sin () dy %3D XCSC

A: Given sinyxdydx-1=yx cscyx, y(1)=0 Dividing both sides by  sinyx dydx-1sinyx=yx cscyx1sinyx…

Q: Ordinary differential equations involve two independent variables and ordinary derivatives.

A: Given, statement is   "Ordinary differential equations involve two independent variables and…

Q: y= Ae* + Bxex

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Q: Subject: Differential Equations 1. y" – 2y' +y = x³ +1

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Q: (3x²y+ 4e³)dx + (x³ + 4xe♥ + 2y)dy

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Q: y (y - 2xy')² = 2 y'

A: Here, the differential equation is given by yy-2xy'2=2y'. Here, the differential equation has to be…

Q: “些。 de e +1 dr

A: Here we will use separation of variable method.

Q: If a population of fruit flies triples every 6 days. What is k, the proportionality constant?

A: The population growth is defined by the exponential equation,  , where k is the proportionality…

Q: Solve the linear differential equation of y' – 2xy = r.

A: Answer :The given differential equation is y'-2xy=xIt can be written as dydx-2xy=x    -(1)

Q: 9. Solve the equation ux + uy = 1.

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Q: differential equations. dy = dr(²yz²+72²)

A: The given differential equation is dy=dx2yx2+7x3x3. We have to find the solution of the differential…

Q: Gy" dx -x(2x? +y)dy-0

A: First make it as in the  form of bernouilli equation  then  simple find the integrating factor then…

Q: y = Ce- 2 + C2e3

A: Given equation is y=C1e−2x+C2e3x......1. We have to eliminate the arbitrary constants. Differentiate…

Q: ot tre eqiatan (X-xy+y?)g'=xy Find the Solutun Rtcon which passes thirongh the point (2,1).

A: The equation is, (x2xy+y2)y'=xy               dydx=xy(x2xy+y2) Take y=vxdiff with respect to x,…

Q: dy dr + y = x

A: We are asked to find the degree of the differential equation.

Q: X Why is it important to know whether a differential equation or system of differential equations is…

A: The given question is solved below.

Q: 2. L{t}= (no formulas)(using the definition of the Laplace Transform)(derive the formula)

A: Let f(t) be a function defined in  piecewise continuous and the improper integral  exists then the…

Q: 13. Find the orthogonal trajectories of y=1. '= X

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Q: (7) d'y dxª -2k² d²y dx² + ky=0 k is a non-zero constant. (This equation arises in bending of…

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Q: Use the eliminatiun methoel t. 2こhoxet,htX differential equations

A: We can write the given system of differential equations as below: 2D-1x+D-1y=e-tD+2x+D+1y=et We have…

Q: 3) (xty-1) dx-(x-y-1) dy=0

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Q: y' = x² y (2 + x³)

A: Given differential equation is

Q: Q/homogeneous differential equation

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Q: Solve Bernoulli differential equation of y + ry = ry².

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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.