Find the particular solution of the initial value problem, 4y" – 4y' – 3y = 0,y(0) = 1 and y'(0) = 5 3x а. 11 y = --e 2 +-e2 4 3x 11 --e 2 4 y = --e 2 4 3X 7 --e2 -+ с. 11 y = 3x d. 7. e2 4 11 y = 2 | 4 b.

Q: Find y'. y = (4x° + 9) (2x7 - 4) OA. O A. 80x° + 126x° – 48x O B. 16x° + 126x° – 48x? O C. 16x° +…

A: y = 4x3 + 92x7- 4y' = ?

Q: 5x Differentiate y= (4x – 3)* * 4x + 1 y' = (4x – 3)5 -60x – 15 y' = (4x – 3)5 - 15x + 1 (4x – 3)5 |…

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Q: 1. 2. rning Find first derivative and second derivative of dependent variable a.y=x²+x+8 b. y=-x²+3…

A: “Since you have asked multiple question, we will solve the first question for you. If youwant any…

Q: Find solution to (4-x²)y'-3x²=2xy with initial value (-sqaureroot 3,2)

A: Topic:- differential equations

Q: Determine the solution of the differential equation y' -y= x*y 3 yi = Cx + * а. уз — Сх + -x4 b. y3…

A: Determine the solution of differential equation:y'-34y=x4y13

Q: Find the general solution for x³y""-3x²y" + 6xy' − 6y = 2x_when_ x>0

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Q: Find the general solution of xy'-2y=2x^2lnx, x>0. write the answer explicitly

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Q: Consider that Let the solution of equation y₁ = x² y2 = 3x² - y3 = 4x-2 2 x² x²y" + xy' 4y = 0…

A: All the parts are solved properly with detailed explanation.Hope you got your answer. If any query…

Q: Solve the IVP, explicitly if possible. 3y x+9(-7)=1 (x– 7)* 8. y=(x+9)3 (x + 9|) yl = (x+9|)

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Q: Find all solutions of the equation x2y' = y3 − 5x2y3 explicitly

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Q: Solve the initial problem: 16y''+8y'+y=0, y(3)=-2, y'(-2)=-4

A: Given ODE is 16y''+8y'+y=0 Consider, 16m2+8m+1=0m=-8±64-6432m=-14

Q: The right hand side of the following first order problem is a linear function of x and y . Use the…

A: Given y′=sin²(x−y),  y(5)=5

Q: Show that y = 5x2 + 2 is a solution to the DE xy' +(2)/(5) y" = 2y.

A: To show: y=5 x2+2 is a solution of differential equation xy'+25y''=2y

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

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Q: Determine whether y = 2x is a solution of the differential equation y'= 6x², a. 6x2- and by'= 6r?…

A: Just take derivative of y and substitute in given differential equation and see if it satisfies the…

Q: x' y' 7x + 6y ||||

A: We have to find the value of x(t) and y(t).

Q: If y=5+ V3x +1, find y' when x = 5. 1 А. 13 В. C. 15 D. 16

A: Given,    y=5+3x+1

Q: Suppose ay″+by′+cy=0 with y(0)=d and y′(0)=k has a general solution y=5e^(3x)−xe^(3x).   What are…

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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: 5. Find a particular solution to the equation -2x y" + 4y' + 4y = xe¯

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Q: Solve the given initial-value problem. x -(: 6 9 -1 12 X" X, X(0) =

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Q: 7. Bonus: Use the change of independent variable r = t² to solve 2ry"+y' + 8y = 0.

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Q: Find a particular solution y'''-y''-4y'+8y=6xe^2x

A: y'''-y''-4y'+8y=6xe^2x Particular integral = 6xe2x 6xe2xD3-D2-4D+8By using property shift F(D) to…

Q: Solve for ‘x’ and ‘y’ where x + y = a – b, ax – by = a2 + b2

A: To solve the equation for x and y.

Q: Find the general solution to (t² + 4)y' + 2ty = t²(t² + 4). Enter your answer as y = .... Use C to…

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Q: 6) а. Find dx if y%3 (n(x + Aj) - А2 х) (/5 В, - 7х) А131 A2=5 В1-4 B2=6 В3-2 DA-1

A: The given function is y = [ln (x + A1) – A2 x] (√5B1 – 7x). The given values are A1 = 1, A2 = 5 and…

Q: Show that y = - In x + 3x - 5 is a solution of y" -=0. Use y = - Inx+3x – 5 to find y' and y". y' =O

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Q: What is the special solution of the equation y0̅ ? y''' + 5y'' + 12y' + 8y =5sin2x +10x2 - 3x + 7

A: Find the attachment

Q: y" + 7y' + 10y = -1lte".

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Q: Find an explicit solution for y′ = ye^−x^2 , y(0) = 1

A: The given differential equation is y'=ye-x2 and the initial condition is y(0)=1. Simplify the given…

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

Q: Which of the following is a solution to the DE y" - 9y' + 18y = 0? O y = Ae^(3x) + Be^(-6x) O y =…

A: The objective of the question is determine the solution of the given differential equation and…

Q: Suppose you want to find an equation for a curve that passes through the point (1, 2x3 2) and whose…

A: We have to solve the differential equation dydx=2x3y to get the equation of the curve.

Q: The particular solution of y" + 10y' + 25y = e−5t is yp(t) = 1⁄2t²e-5t Find the null solution yn (t)…

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