Show that y₁ = ecos(2x) and y2 = e sin(2x) are two linearly independent solutions of d'y dy dz² +2- dz + 5y = 0

Q: 4x +1 = cos y?

A: According to guidelines we should have been able to solve only one question at a time

Q: dy du du' dx' dy dx y = u53 and u = 5x4 - 2x² ind and

A: This is question of calculusHere differentiation given We have to do it.Further calculation is given…

Q: 2. Reduce to an exact equation and solve it: dy_2xsin 2 y+(2siny)/x² dx 2x²cosx-(2cosy)/x (2x²ysin…

A: GIVEN: dydx=2xsin2y+(2 siny)/x22x2cosx-(2cosy)/x             (2x2y siny -x y3sinx)dx +(x3siny +x3 y…

Q: Solve the non linear DE: 2y’’=2yy’

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Q: show that the solution y(t)=e^2t(cos(t)-2sin(t)) is linearly independant.

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Q: Find dy/dx at the point (2,1) if 4y3-x2y2=0

A: Given that: 4y3-x2y2=0

Q: dy du du' dx dy dx y = u53 and u = 5x4 - 2x² Find and

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Q: show that the solution y(t)=e^2tsin(t) is linearly independant.

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Q: Find the general solution of the D.E. (y^2 - 2xy + 6x) dx = (x^2 - 2xy + 2) dy = 0 Show your…

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Q: Find the general solution of the Bernoulli equation 2yy′= y^2+ t + 1.

A: To solve given differential equation first we solve for rearrange the equation in the form of first…

Q: 11) Find a function y-f (x) that satisfies both conditions: d - 6x -4x+5,f(-1) =3 dx %3D dy 2 3 ==+…

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