-(D² – 25) y = x e* . Using method of undetermined coefficients, what is y Consider A ' = Ax e* + B e*

Q: What are the P(x) and Q(x) of y' =y-xy³e2Xrespectively?

A: Given the differential equation is: Since

Q: Eliminate the constant: 2x 3x =c₂₁e²x + c₁₂e³x Oy"-y'-6y=0 Oy"-5y'+6y=0 Oy"+y'-6y=0 Oy"+ 5y'+6y=0

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Q: If y = u³ - 4 and u = 3x² + 10, find y' O 18x(3x² +10)² O 3x(6x² + 10)² O18(3x² +10)² 6x(3x² +10)² घ

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Q: Find the solution of the DE using variation of Parameters y''' - 3y'' + 3y = (ex/x)

A: The given problem is to find the solution of differential equation using method of variation of…

Q: 3. y=√√2x (x²-2), y'=?

A: We have to find the derivatives.

Q: Use Euler's method and 4 steps to approximate y(1)

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Q: Find the general solution of x(x + 3)dy = 2dy + √(9- y²)(12x + 9 + 4x²) dx.

A: We will separate variables and then will integrate it to find general solution of given differential…

Q: 1. Let y = x2 + x +4+ Find y'.

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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: Show that the function f(t) = 1² – } is a solution of the dif- ferential equation (y')² – 4y = 2.

A: Given:       f(t)=t2−12.Differential equation is: (y')2−4y=2

Q: (1-xy)-² dx + [y² + x²(1 - xy)-²] dy = 0; -2

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Q: Find y'. x3 +yở = 8£y

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Q: (1 – x)y" + 2xy' = 0 , y1

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Q: 3. (4r*y² – 6r²y – 2r – 3)dr + (2r^y – 2r)dy = 0, y(1) = 3

A: The given equation is exact.

Q: Solve by reduction of order. Find y2 and y (x² + 1)y" – 2xy' + 2y = 0 yı = x -

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Q: Suppose that Yı x5 is a solution to x²y" – 10xy' + 30y 0. Use reduction of order to find another…

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Q: 8.) y" +2y' +5y = 3e 2* ; and y(0) = y'(0) = 1

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Q: ye x, (21x) satisfie s Show that the equation

A: Given: The given equation is xy''+n+1y'+y=0  ,  y=xn22x

Q: y(4) - 4y" + 6y" - 4y+y=0; y(0) = 0, y'(0) = 1, y'(0) = 0, y" (0) = 1

A: The Laplace transform is used to find the solution of the linear ordinary differential equation with…

Q: Find y': y=V5+2 — 2 O y = 7-2x 2√5+2x-x² Oy = √2-2x 1 Oy = 2√5+2x-x² 1-x O y = √5+2x-x2

A: We have to find derivative of given function.

Q: 8. x(x² + 1)y' + 2y = (x² + 1)³

A: Given problem:- xx2+1y'+2y=x2+13

Q: Find y as a function of a if y(1) = -4, y'(1) = -9. y x²y" + 2xy' - 6y = 0,

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Q: Solve the IVP: X' = AX, where -2 1 A = -5 0 3 -2 and -2 X(0) = -1 2

A: To find the solution of X'=AX where, A=−210−50003−2X0=−2−12

Q: Answer: y = -(e-x + c)/(1 + x2)

A: Given differential equation is,

Q: 2. y" - 3y' +2y = e4x + 6x³ – 2+ 3sin(4x) | |

A: See 2nd step

Q: y (2 xy +1)= xy'

A:

Q: 2.ryy' = y? - 2x. Find the solution that passes through the point (1,2).

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Q: can you explain if this is true or false if y=x2+y2, then y'= 2x+2y

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Q: Q4- Solve y"- 4y' + 13y 3x.e*

A: Topic:- differential equations

Q: x²-2x* 5. Integrate with respect to x x4

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Q: Solve the IVP: X' = AX, where -() xw - () 3 -3 1 A = 2 -1 0 1 -1 1 and 7 X(0) 4 3

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Q: Inx+1 dy will be dx If y = then 2x3 – 3x' (2x³ – 3x) +1) –- (In x + 1)(6x? – 3) А. (2x³ – 3x)² (2x3…

A: Using derivative rule of (u/v),

Q: 3/(a) Let X × b(n, –) and E(x)= E(16–7x) find n.

A: Solution : Given : X ~ b( n, 14 )             E(x) = E( 16-7x ) To find n : It is known that for…

Q: Eliminate the Arbitrary Constant: y = c,x² + c2e¬* а. 2(х + 1)у' — (x? — 2)у" — х(х + 2)у %3D0 b.…

A: topic - differential equations

Q: y" + 6y' + 9y = 7+ e-4x

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Q: Use the substitution y = xm to find the general solution to: x2yn - 2xy' - 4y = 0. Show all of…

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