If J(x) satisfies the differential equation xy" + y' + xy = 0 and J(0) 1, then J'' (0) is -/3

Q: 2xy'-y= Iny'

A: Given,

Q: Show that if P(x) #0 the differential equation y' + p(x)y = f(x) is not exact differential equation.…

A: y' + p(x)y = f(x) can be written in the appropriate form dydx + p(x)y = f(x)  ⇒dy +p(x)y dx = f(x)…

Q: Solve x*y"- 2x(1+x)y'+2(1+x)y= x'

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Q: Is y'' = sin x a linear differential equation?

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Q: Find a differential equation for y=c1e^9t +c2e^-4t. Oy"+5y'+36y=0 Oy"-5y'-16y=0 Oy"-5y'-36y=0…

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Q: y = (x + y – 1)².

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Q: Identify the linear differential equations. Justify and show work.  1) y''=ex 2) y''= ey 3)…

A: Hey, since there are multiple questions posted, we will answer first question. If you want any…

Q: Verify that the indicated function is an implicit solution of the given differential equation.…

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Q: Identify whether the following differential equation is separable or linear. 2y x² +: Jax = (3–…

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Q: Find the differential equation whose general equation is y = C₁x + c₂ex. A. (x-1)y" - xy' + y = 0 B.…

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Q: Solve the differential equation for the motion of the spring 384x''+1152x'+864x=0   if x(0)=-2 and…

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Q: 4x3 y = x", y(0) = -3 and choose the correct answer from the followir x4 +2 Solve the initial value…

A: Note-  Acc. to Bartleby guidelines, we are supposed to do only one question. If you want more to be…

Q: What is the differential equation of 2y'=3y+1 when y(1)=0

A: Consider the provided D.E 2y'=3y+1  when y1=0 We need to find the solution of the given D.E, Since,…

Q: Let y(x) be the solution of the differential equation dy * (* 2) = x; y(1) = 0, d = 0 dx then y(2)…

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Q: The solution of the first order linear differential equation y' + ycotx = cosx is O…

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Q: Please help write the ordinary differential equation below in the form x’=Ax+f

A: Given that the ordinary differential equation is y'''+2y''-4y'+y=5tWe have to write this in the form…

Q: Consider the differential equation y'' + 6y' +9y = 0.

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Q: Find the general solution of the DE (x + y)dx + (x - y)dy =0.

A: Given differential equation is(x+y)dx+(x-y)dy=0Here, M=x+y and N=x-ythen ∂M∂y=1 and…

Q: Solve for the differential equation of the given function y = C1x + Cze* by applying elimination of…

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Q: Match the differential equation with its direction field. y'- sin(10x) sin(10y) 20) -0.3 1-0.2 1…

A: Remark: We know that the slope field is a graphical representation of a differential equation. This…

Q: What is the differential equation of the family of parabolas with their vertices and foci on the y –…

A: We need to find differential equation of the family of parabolas with their vertices and foci on y -…