The linear, homogeneous, constant coefficient differential equation of least order that has 32 y=-3e +5e sin (25 as a solution is: ) Oy) - 10y(4) +37y" +52y = 0 -) Oy)+2y-11y" +52y=0 Oy)+2y-lly" - 52y = 0 Oy"-2y+37y - 52y=0

Q: Find the linear, nonhomogeneous differential equation with constant coefficients whose solution is y…

A: Given solution to a linear non-homogenous differential equation is    yt=c1et+c2e2t-3tet+cost-e-t2…

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Q: 141: Find the general solution of the given ordinary differential equations. a) y" +4y' + 7y = 0 b)…

A: a) y"+4y'+7y=0 Auxiliary equation is  m2+4m+7=0⇒m=-4±16-472⇒m=-4±232⇒m=-2±3 So, the general solution…

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A: Solved below

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A: We are given the solution as : y(t)=c1et+c2e2t-3tet+cos t-e-t2 ---(1)…

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A: Here we can use the fact that  D+an+1 annihilates xne-axD2+b2n annihilates xnsinbx

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A: Solution ) we have option 3rd  y"+ 4y = 0 Auxilliary equation  m2 + 4 = 0 m2 = -4 m = √( -4 )  m =…

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Q: Find a homogeneous linear differential equation with constant coefficients whose general solution is…

A: ........(i)Differentiating equation with respect to x So, .........(ii)

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A: (1) let the differential equation be y''-8y'-15y=0 auxillary equation D2-8D-15y=0 now, ⇒m2-8m-15=0…

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Q: Find the linear, nonhomogeneous differential equation with constant coefficients whose solution is…

A: Given: yt=c1et+c2e2t-3tet+cost-e-t2                                      ..1 For finding solution of…

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Q: 5. Use the meyhod of undetermined coefficients to solve the differential quation. a) y" + y + y = x²…

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