Obtain the genral solution to (D5-15D³+10D² +60D-72)y=0 y=e²x(C₁ + C₂x) + e-³x(C4+C5x) y=e²x(C₁+C₂x + С3x²)+e³x (C4+ C5x) y=e-2x(C₁+C₂x + C3x2)+e-3x(C₁+ C5 Oy=e²x(C₁+C₂x + C3x²) + е-3x(C₁+C5X

Q: 2) Use y = ax to solve 2'y" - xy' + (x+1)y=0.

A: The given differential equation is: 2x2y''-xy'+x+1y=0. We have to solve using y=∑n=0∞anxn+r.

Q: Find all functions y satisfying y" + y" = y' + y. You may use the factor- ization x + x² – x - 1 =…

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Q: Solve the particular solution (D2+3D+5)y = 5e-xsin2x using  D- operator method.

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Q: Q/IF it was AY ₁2) = -12 Y(2) ℗ Y³ (2) = − 12 ⒸY² (2) = -11 Y³ (2) = -11 DÝ (2) = -13 © ²³ (2) = -13…

A: Given

Q: x2 + 2y2 + 3z2 = 1

A:

Q: A/If x² (y - 4z) - y²(2x + 3z) + z²(3x - 4y) = xyz Find Zx

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Q: u" - 16u = 0

A: Given the differential equation is u" - 16u = 0. Here the auxiliary equation is m2 - 16 = 0

Q: 2:2 + [3] x + 2 = [0] in Z6.

A: The solution given below with attached file.Explanation:

Q: Solve the following linear differential equation system, i.e., find y₂(t). dyn (1) dt dyż (t) dt =…

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Q: d?y dx3 Solve - 27y=0 O a. y = ce -3x + e7*(c2cos- 3/3 x+C3sin 3/3 -x) 2 Ob. OBy=c,e3x +e"(c,cos 33…

A: We have to solve given problem:

Q: Transform ϕ (xmyn) ydx + ψ (xmyn) xdy = 0 to the type variables separable by the substitution z =…

A: Given differential equation is 2+4x2+yydx+x3ydy=0......1. Compare equation 1 with Mdx+Ndy=0, we get…

Q: Solve for the general solution of (D: - 5D + 6)y = 4e* using method of undetermined coefficients.

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Q: If x, y belongs to Z prove that the equation x^2+4x-8y=11 has no solution

A: The given equation is, -----(1)

Q: Find the solution of 4x²y" - 6x²y + y = 0, x > 0 of the form Y₁ = x¹(1+₁x + €₂x² + 3x³ + ...) Enter…

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Q: If y=x* - 5x² + 2x – 3 then equals dx A x* - 5x² + 2 В 4x – 10x+ 2x – 34 4x - 10x+ 2x D 4x - 10x+ 2…

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Q: 6. (t -1)+(2 8. (2x² +5xy+ 3y²)+(8x² –7y²)

A: 6.

Q: Find two linearly independent solutions of 2x²y" - xy + (-4x + 1)y=0, x > 0 of the form y₁ = x¹(1+…

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Q: y₁=1+a3x³ + arº +... Y₂ = x + b₁x¹ + b₁x² + ... Enter the first few coefficients: a3 = a6 = b₁ b7 )…

A:

Q: Ify= (x³ + 1)“ , theny = ? (A None of the given choices B(3x2)? © 2(x³+ 1) O 6x²(x³ +1) E 2(3x² + 1)…

A:

Q: 7. Verify that y = x2 - 1 is a solution of (y')* + y? = -1.

A: Given- y=x2-1 To verify- That the above function is the solution of y'4+y2=-1.

Q: Find the general solution of ди ди (y – z) + (x – z) ди + (2y – 2x) ду - az

A: The differential equation is given as (y-z)∂u∂x + (x-z)∂u∂y  + (2y-2x)∂u∂z = 0 We will solve it by…

Q: Find x, y, z, and w. X = y = Z= W = x 7 (2x y 6 - 5) (2x = ¹) ] - [ (²x - ² 9y Z 9 By + 8) ] 8 (w +…

A:

Q: Which of the following is the general solution of x 2 V) 2 -xy'-56x 2 =0? O a.…

A: We have to solve given problem: Note: given differential equations is wrong. According to options…

Q: Solve (2x + 1) dx (x + 3y + 2) dy = 0

A: The given differential equation is

Q: Select all equations that are equivalent to a-6z 16. a + 6x 9 0 O b a + 6x +9 = 16 Oc a+6x + 9 = 25…

A: Solution:-Given equation,     x2+6x=16  —1let us see and solve each option given,a…

Q: Find dydx for…

A: the given equation of the curve is: y3+y2-5y-x2+4=0 we have to find the value of dydx

Q: 7. (x+2yXdx- dy) = dx + dy. %3D

A:

Q: y"' – 3y" + 4y = 6+80cos(2x)

A:

Q: 1.² T 20 40x-x² 9√x²+y2 dydx=

A: We have to solve ∫020∫x40-x29x2+y2dydxThe region bounded by0≤x≤20x≤y≤40x-x2⇒x=y and y=40x-x2squaring…

Q: ) Find the general solution (4x + 2y +3)dx + (6x + 3y- 2)=

A: