Find the differential equation given the general solution: y = cer + Czex + 3x

Q: y" – 2y' + y: [12x – 4]e-Sx %D -

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Q: Solve the given differential equation by undetermined coefficients. y" + y' = 8 y(x)

A: The solution to this differential equation can be written as the sum of the complimentary solution…

Q: Solve the differential equation for y in terms of x 1) y' + xy = 2x

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Q: Solve the differential equation- ydx + x (1+y) dy= 0

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Q: Solve the given differential equation by separation of variables. dy yex -e-y = e-2x-y %3D dx

A: The differential equation is given as…

Q: 3. y?dx + (x² + 3xy + 4y²)dy = 0; when x = 2,y = 1

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Q: Solve the differential equation by variation of parameters. 4x e2x y(x) = = y" - 4y =

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Q: Solve the differential equation by variation of parameters. y" + 2y + y = et In(t) y(t) = Submit…

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Q: y= C,e*+ C2e¬x

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Q: y(4) + 2y" + y = (x – 1)?

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Q: Solve the given differential equation by separation of variables. dy eY + e dx -5x - y

A: Solve Differential equation by variable separable method

Q: Find the differential equation y = ae x + blnx + cx + d

A: Given that: ‘y=aex+blnx+cx+d…

Q: Find the differential equation whose solutions correspond to the following equation. y = C1x^2 +…

A: For the solution follow the next step.

Q: yJzスこナる dy t xJ (A ZXZ+3

A: given differential equation is variable separable differential equation we will first separate the…

Q: Find the differential equation whose general solution is y = A + B e^(- 4x)

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Q: Solve the given differential equation by separation of variables. xdx = 2y y =

A: Use Separation of Variables to solve the given differential equation xdydx=2y

Q: Give the differential equation that has as its general solution. y = C₁ sin(2x + C₂)

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Q: a. y = C,e=x + Cze-2x + x

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Q: 2xdy + y Cyz Inx -1) dx = 0

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Q: Find the differential equation whose general solution is y = cvh x + cv2 e^x %3D

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Q: Find a differential equation whose general solution is y = c₁est + c₂e-2¹. 5t = 0

A: I have given the answer in the next step. Hope you understand that

Q: Solve the given differential equation by variation of parameters. y'' − y' = xex

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Q: y= C,sin2x+ C2cos2x

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Q: Find the differential equation having the solution as: a. y = C,e¬x + C2e¬2x + x b. y = C, + C2e³x

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Q: Solve the differential equation 3y' = x + y by making the change of variable u = x + y.

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Q: 2y²e»* dx + 2xyey° dy = 0

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Q: Solve the differential equation by variation of parameters. y" + 3y + 2y = 8 1

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Q: Solve the differential equation by variation of parameters. 1 y" + 3y' + 2y = 6+e* Show all your…

A: Use the procedure of method of variation of parameters to solve this problem.

Q: У - 2у+ %3D 1+ x

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Q: 8. x csc ) - y] dæ + xdy = 0

A: Given the differential equation

Q: Tx?+y?)dx + 3xydy

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Q: Find the solution, using variation of parameters, to the differential equation (D3+D)y = sec2x.

A: Given :- The given differential equation is  D3 +Dy = sec2x Let the equation be  d2ydx2 +Pdydx+ Qy…

Q: 5y*y' = x?y' + 2xy

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Q: Solve the given differential equation by separation of variables. exy dy =e-¯V + e-8x - y dx

A: In this question, we want to solve the given differetial equation using separation of Variables.

Q: Solve the differential equation 9y' = x + y by making the change of variable u = x + y.

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Q: Find the differential equation having each equation as general solution. 7.) y= x + C,x + C,e 11.)…

A: An ordinary differential equation is an equation containing independent variables, dependent…

Q: y +y=}(e* – e*)

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Q: Solve the differential equation by variation of parameters. 1 y" + 3y' + 2y =: 3 + e* y(x) =

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Q: y = cje + c2er

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Q: ry? V1+ x²

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Q: solve the differential equation and express final answer with the value of C (3x^2 +y^2) dx + 2xydy…

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Q: Find a differential equation whose general solution is y = c₁e5t + c₂e-²t. = 0

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Q: O y"+y= secx cosecx %3D

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Q: Find a differential equation whose general solution is -4t y = cjet + cze¬4.

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Q: Solve the given differential equation by variation of parameters. y" - y' = xe*

A: Given y"-y'=xex

Q: x²(y+: x(2y+

A: The differential equation is x2y'=4x2+7xy+2y2. Divide by x2 on both sides, y'=4+7yx+2yx2 Substitute…

Q: Solve the differential equation by variation of parameters. y" + 3y' + 2y = 3 + e* y(x) =

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Q: (2x+ykdx– 3(2x+ y+4)dy=0 1.

A: Note: We are required to answer only the first question, unless specified.

Q: Solve the given differential equation by undetermined coefficients. y" + y" = 8x2 y(x) = %3!

A: The solution is given as

Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.