Q1/ find the solution to + (1-4h?)y-ein(2n) -0 %3D y(0) = 0.2.

Q: Find the solution of dy e y- dr ey +e-2x-y

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Q: Is y = e-x + 2xe-* a solution to y" + 2y' + y = 0.

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Q: (D² + D)y =x+| ;

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Q: Obtain the general solution C. (D2 + 2D + 2)y = e-x

A: Obtain the general solution C. (D2 + 2D + 2)y = e-x

Q: Find the solution of the D.E. below: 2(2x² + y*)«x – xycdy = 0 ... x* = c (4x²+y²) x* = c(x?+ 4y?) B…

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Q: Find the general solution of (T^2 + 4)y' + 2ty = t^2 (t^2 + 4) with the variation of parameters…

A: In this question, we find the general solution of (t2+4)y'+2ty=t2(t2+4) with the variation of…

Q: Determine if y(x) = e-3x is a solution of y" + 3 y' = 4y

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Q: Find general solution of " – y – 2y = e2t

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Q: Find the solution of y'' (x) = y(x) that fits in origo and goes through the point (ln2,(3/2) )

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Q: у" — у' — х %3 0

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Q: Solve for Yp * y" – 9y = e3x

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Q: Find the general solution of y" – 3y' + 2y 1+e-x°

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Q: | 2x²+ 4x- 5 x(x² +6x+10)? * To solve | -dx using the method of partial fractions, we write it as

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Q: Determine whether y=x-1 is a solution of V)'+y=-1

A: Given y=x2-1, taking derivative with respect to x. ⇒dydx=ddx(x2-1)⇒y'=2x-0  ∵dydx=y'⇒y'=2x…

Q: Find the general solution of (D3-D2+D-1)y = 15sin2x using method of undetermined coefficient.

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Q: Find the General Solution: y" - 3y' + 2y =e*

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Q: (D + 2)x + (D + 4) ỵ = 1 (D + 1)x + (D + 5) y = 2

A: Given simultaneous equation is D+2x+D+4y=1    (i)D+1x+D+5y=2    (ii) Eq. (i) can be written as…

Q: Find the general solution to y = -e*y² + y +e²

A: Given first order differential equation is solved by using integrating factor.

Q: What is the solution of y2 - x2y'=0 with IVP y(1)=1/2 ?

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Q: Find the particular solution of y''-5y'=x-2 when x=0, y=0, y'=2

A: Given that that a non homogeneous differential equation and we find its solution.   Here i attached…

Q: 2xyy' 1+ y2 What is the general solution?

A: The solution is given as

Q: determine the particular solution of: y"-4y'+3y=e^t +t^2

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Q: Find the particular solution. y' = e* - 4; y(0) = 3

A: For a differential equation, there are two parts of solution. one is the complimentary function…

Q: Check that y Cx) = e* is the Solution of y" + y' - 2y = 0

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Q: Solve for the solution of: (D3 + D)2y = 0

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Q: 11. (D- D)y = 0.

A: As per our guidelines only one question can be solved. Please find the solution for Q no 11 below:

Q: Find the general solution using variation of parameters. - 4y + 4y = (x + 1)e²-

A: To solve the following problem

Q: Q4: Solve the initial value problem: ty' = 2y + t³

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Q: Find the general solution of y'' - 2y' - 8y = 24(x2+1)e4x by using VARIATION OF PARAMETERS

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Q: 4. Solve the IVP y' = 2x-3y +e¯* y'= 2x- 3 y +e * with y(0) = 1 y(0)= 1

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Q: y"+ 4y = x What is the particular solution y.? Yp

A: helar we have to find particular solution of the given differential equation. the solution is…

Q: y' = - 2xy

A: The given differential equation is y'=-2xy⇒dydx=-2xy The given differential equation can be solved…

Q: HiW.2 DE solve y=ソ-4y A.e |-4y

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Q: Find the general solution to: 3X y^ - Gy' +Qy= x*e*

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Q: Q4\ Solve by Gaussian elimination x-4y-2z = 21 2x+y+2z = 3 3x+2y-z = -2

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Q: Find the general solution 5. (D² – 1)y = 0

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Q: Two solutions of y"-2y'+y = 0 are e^-x and 5e^-x. Is the general solution y = cle^-x + c25e^-x?…

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Q: Obtain the general solution of the homogenous L.D.E (D³-14D+8)y=0

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Q: Q2/ Show that y =e2x + e-3x is the solution to the y"+ y' - 6y = 0

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Q: find the general solution of y''+2y'-3y=(5x^2-7)e^-x

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Q: Specifically a differential equations problem. Question in pic below.

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Q: Find (a) the general solution and (b) the particular solution for the given initial condition. 8 y'…

A: Given Data: Differential Equation: y'=8x+6x4-2x6 ......1 Initial condition: y1=8

Q: 4. Find the constant a so that Ø(x) = xe2x is a solution to y' + ay – e2x = 0 А. 4 В. 1 C. -1 D. -2

A: We have to find a

Q: 4. Solve (x-2)y" - (4x-7)y' + (4x-6)y= 0, if y₁ = e2x is one known solution? HO The Cystem 2e²t

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Q: y" - 4y' =t+ 3cost + e -2t

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Q: ds Find the solution 2- dt S 5t3S3

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Q: Find the particular solution of (d2y/dx2) = 4x3 - 2x; y' = 4/5 and y = 1 when x = 1

A: Given differential equation, d2ydx2=4x3-2x       ...(1) y'=45 and y=1 when x=1

Q: Obtain general solution of the D.E. y' + (1/3)y = e%y4

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Q: find the solution of y''-2y'=x - e^3x

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Equations and Inequations

Equations and inequalities describe the relationship between two mathematical expressions.

Linear Functions

A linear function can just be a constant, or it can be the constant multiplied with the variable like x or y. If the variables are of the form, x2, x1/2 or y2 it is not linear. The exponent over the variables should always be 1.