Find the particular solution of the initial-value problem y'"'- 4y=12x; y(0) =4, y'(0) =1 A y=3e + +3x ® y=3+e=2 = 3x c) y=3+e¬2* +3x D y=3e2*+e-2x _ 3x

Q: Solve 4y'' + y' – 3y = 0, y(0) = - 4, - 4, y'(0) = 0.5 y(t) =

A: The given differential equation is second order linear homogeneous differential equatio. So firstly…

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Q: (x^2)y''-2xy'+2y=0; y(1)=4, y'(1)=7   Find particular solution that satisfies the given condition

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Q: c. y' + 2y = x³ with y(1) = 2 Yo (x) = e Yp (x) = y (x) = y (x) = -2x 1½ e ²x³ - 2/ ( 10²x² -…

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Q: Solve y'" – 4y' + 20y = – 68e*, y(0) = 0, y'(0) = 0| - y(t) :

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Q: Find the general solution (D^3 + 7D^2 + 19D + 13)y = 0 when x = 0, y = 0, y' = 2, y'' = -1

A: Find the general solution (D^3 + 7D^2 + 19D + 13)y = 0 when x = 0, y = 0, y' = 2, y'' = -1

Q: Solve (x² + 4)y' = 2xy In|x] = In(y? + 4) +C O Option 1 Inlyl = In(x² + 4) +C

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Q: 5. Find the general solution of the equation _ x² + y² Z (y-x)p+ (y + x)q=

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Q: Find the general solution to the nonhomogeneous equation y″+10y′+25y= 2e^t +2e^-5t

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Q: Find the general solution

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Q: Find the solution of with y(0) 4 and y'(0) = 7. y = 4e^(-5t)+27te^(-5t)+7e^(3t) y" +10y + 25y = 448…

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Q: Solve the initial value problem (1+ x²)y" + 4y = 0, y(0) = 0, y'(0) = 12. If the solution is y = k=0…

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Q: y' =xy

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Q: 3. y' = 5y + e-2*y-2 y(0) = 2 У (0) - 4. хуу' + 4x2 + у? 3D 0 о у(2) 3 —7

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Q: (3x - 1)y" (3x + 2)y' (6x8)y = 0, y(0) = 2, y'(0) = 3; y₁ = e²x

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Q: 3. x'= -2tx + y, y'= 3x-y

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Q: 4 y'+− y = 2; y(1) = −4 {y= X 2 = 5 -x-- 22 X 5

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Q: x²y"-9y" + 6y' - 9 = x² + 6x y'(0) = 0

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Q: Solve the DE xy(y² + 1)dx + (x²y² - 2) dy; y(1). = 1 O x^2 (y^2 - 1) = 2 - 4ln(y) O x^2 (y^2 + 1) =…

A: Here we have to solve the differential equation.

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Q: 5. x' = 3x - y, y' = x + 2y

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Q: Find general solution   y’’ + 2y’+ y = 2e^-t (t)^-2

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Q: find the solution yl-3y'+2y=e3t , y'(0)=0, y (0) =1 el-2e2t+ e3 t .a 1 3et-2e 3t +-e .bO 2et-3e…

A: We will solve the differential equation using standard methods

Q: Find the solution. xy'+ xy = 1 - y, y(1) = 0 A y = x-'(1 – e!-") y = x-2(1 + e'+*) © x=y-'(1 + e'-1)…

A: Given differential equation is xy'+xy = 1-y, y(1) = 0

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Q: The particular solution (yp) of the equation y" - 3y + 2y = 5 e* is yp = -5xe*

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Q: In each of Problems 9 and 10, solve the given initial value problem and determine at least…

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Q: Can you substitute equation 28 into equation 27 and try to achieve equation 30? Please I need it…

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