y = c1 sin3x + c2 cos3x is the general solution of the differential equation      y "+ 9y = 0. The particular solution that satisfies the initial conditions              y (π / 6) = 2, y '(π / 6) = 1 is:

Q: Find the general solution of the differential equation y" + 2y' + 4y = e* sin 2x + æ?

A: the given equation is  y''+2y'+4=exsin2x+x2 Auxiliary equation corresponding to the equation is…

Q: (a) 2xy? + x²y' = y², y(1) = = -1 (а) Зу(2? — 1) + (»3 + 8y — За) dy (b) 4x?3 dy гу* + 2 dæ (e) xy'…

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Q: Verify that the given function is a solution of the corresponding differential equation. d2y/dx2…

A: Here, we are given the function, y = e−2x(cos3x+sin3x). Now, we need to verify whether the given…

Q: Find a first order differential equation for which y2 sin(xy) + (2xe)cos(x)) = 3 is an implicit…

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Q: у" + 25у %3D 5 tan? (5x) сos(5x) 2.

A: Given the DE is y''+25y=5tan25xcos5x. To solve this DE use the variation of parameters method.

Q: Find a particular solution y, of the differential equation: (a) 2y" + 4y' + 7y = x2 (b) y" + 9y = 2…

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Q: The solution of the differential equation subject to the initial conditions y(0) = 0 and y'(0) y(x)…

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Q: Solve the differential equation by variation of parameters. y"+y = n²(x) xx) = c₂cos(x) + csin(x) +…

A: The solution is given as

Q: Solve the ordinary differential equation 3xy" + (2 - x)y' - 2y = 0. Then evaluate the first four…

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Q: Consider the differential equation: y" – 6y' + 9y = (x + 1)e3* Determine the function „, for the…

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Q: Solve the differential equation by variation of parameters. y" + y = sec (0) tan(0) y(0) = c₁cos (0)…

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Q: Do the functions y₁ = cos5t and y2 = sin5t constitute a fundamental set of solutions of the…

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Q: Solve the ordinary differential equation 4xy” + 3y’ +3y = 0. Then evaluate the first four terms of…

A: Given ordinary differential equation is 4xy''+3y'+3y=0

Q: Solve the ordinary differential equation 4xy” + 3y’ +3y = 0. Then evaluate the first four terms of…

A: To solve the ordinary differential equation: 4xy''+3y'+3y=0      ⋯1 Then to evaluate the first four…

Q: Solve the ordinary differential equation 4x²y"+(1-2x)y = 0, Then evaluate the first four terms of…

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Q: Solve the differential equation by the method of integrating factors. y + 7y = cos (e7*) y = Use "C"…

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Q: y" +y = cos x ; when x = = 0, y = 0,y' = 1 %3D

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Q: Solve the ordinary differential equation  3xy” + (2 - x)y’ - 2y = 0 . Then evaluate the first three…

A: Given differential equation is 3xy''+(2-x)y'-2y=0                         (1) ⇒y''+2-x3xy'-23xy=0…

Q: Solve the ordinary differential equation 3xy” + (2 - x)y’ - 2y = 0 . Then evaluate the first three…

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

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Q: y' = 4x(2y-³-y)

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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.