1. The complementary equation to dt² + dy + 4y = 5e-³t is:

Q: Find the general solution of the equation x(y2 + 1)dx + (1+ x²)dy = 0. A. In(x2 + 1) + 2Arctan y = c…

A: The given equation is; x(y2+1)dx + (1+x2)dy =0

Q: give me the solution of   y'' - 2y'- 2y = 0

A: Topic:- differential equation

Q: Use method of undetermined coefficients. y" − 2y' +2y = 2x — 2.

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Q: Find the particular solution of the given D.E. (y²-2xy + 6x) dx + (2xy - x²-2) dy. =0 when X=-2 and…

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Q: Find the general solution of the given equation y" + y = 0

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Q: Consider the two ODEs dy dx dy dx +y=0 + y² = 0 equil eq.2 (a) How are the two equations different…

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Q: 3. Consider the equation (3x2 + 3y? + 6) dx + (kxy + 8y³ + 1) dy = 0. (a) Determine the value of the…

A: The solution is given as

Q: Solve the Euler- Cauchy equation

A: We solve the given differential equation using Euler cauchy method.

Q: 3. Solve the following Bernoulli's equations: (a) il (xxzy) 21 dy -5 dx +9y = y³e³2r

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Q: Convert the given equation into the form of a Sturm-Liouville equation. y" +7y' + ay = 0 Write the…

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Q: x² = 2y²(y-1) y² = 2x²(x+1) x² = 2y²(y+1) y² = 2x²(x-1) dx (3x²-2-²) 4

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Q: Find a general solution of the equation: 3x?y" + 2xy' – 2y = 0

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Q: Find a constant solution of y′ = t2y - 5t2.

A: we have to find a constant solution of  y'=t2y-5t2

Q: Find a particular solution to y" + 5y + 4y = -10te". Yp =

A: Given the D.E. y''+5y'+4y = -10te3t We have to find particular solution yp of this equation.

Q: Find a particular solution to

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Q: Determine the appropriate form for a particular solution of the fifth-order equation(D - 2)3 (D2 +…

A: Given differential equation is D−23D2+92y=x2e2x+xsin3x......1. We have to determine the appropriate…

Q: Find the general solution using substitution of each of the following DE: 1.) (2x + y + 6) dx + (2x…

A: As per our guidelines, we are supposed to solve only first question. Kindly repost other question as…

Q: 1. х2у" — 20у%3D 0

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Q: 8. Solve the Cauchy-Euler equation 4x²y" + 8xy' + y = 0.

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Q: Find the general solution of the DE.

A: dydx-2ycot2x=1-2cot2x-2csc2x

Q: Find a particular equation for the DE: y+4y'-2y= 2x -3x+6

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Q: differentiate the following: Q(y)= y3/3 + 3/y3

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Q: 2 Find the general Solution of yty = 2xcosx -CosX %3D

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Q: O Show that the substitution r = e' reduces the equation ax?y" + bry/ + cy = g(x) to an equation…

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Q: Solve the IVP by substitution. (3x2 - 2y2)y' = 2xy;  y(0) = -1

A: Substitute  x = vy and than solve using method of separation of variables.

Q: Solve y" – 4y' + 6y = 8(t – 3), y(0) = 0, y'(0) = 0. -

A: Use Laplace table.

Q: Evaluate the polynomial by finding the value of y when x = 2. If decimals, use 8 decimal places. xdy…

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