Find the general solution of the differential equation y – e³x+y = 0 using separation of variables. %3D

Q: x² y' - 2lnx - e2y+4(Inx)/x = 0

A: Given: The given differential equation is x2y'-2lnx-e2y+4lnxx=0

Q: Solve the differential equation: dy/dx = 2 + sqrt(y -2x + 3)

A:

Q: "-y = x e* Cos?x

A:

Q: dy - 2y + 6 Find the solution of the differential equation. - dx 2.x + y + 2 ||

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Q: Find a differential equation whose general solution is y = c₁e²t + C₂e-2.

A: Note: Your general solution should be: .The differential equation for this general solution needs to…

Q: Find the differential equation given the general solution: y = cer + Czex + 3x

A:

Q: Find the differential equation whose general solution is y=c1e4t+c2e-5t

A: Find the differential equation of given solution.

Q: d²y dy e* - 2 + 2y = dx² dx cos(x)

A:

Q: dy = -y + 2 with the initial value y(0) = -2 dx

A: Explanation of the answer is as follows

Q: (d) (x2 + y²) dx – 2xydy = 0 (e) y' + 2xy = 10x (f) (y – 1) sin xdx – dy = 0 -

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Q: Find the linear differential equation that is satisfied by y=xe-xsin3x+2e-xcos3x.

A: Let's find linear differential equation.

Q: -3z y" + 6y' + 9y = for a> 0.

A:

Q: y(3) + y" – 2y = xe¬*

A:

Q: x" + 2x' + x = e° -t.

A:

Q: -dy x + 3y²/x2 + 1- = 0, dx y(0) = 1

A: The given differential equation is a variable seperable equation which can be solved as shown...

Q: Find the general solution of the differential equation.

A: According to the given information it is required to solve the given differential equation:…