Find the value of x in the equation, 2x + j4y-3 = j3x – y – j10.

Q: Q4. Find the values of the constants a, b, c so that - F = (axy + bz³)ī+ (3x² − cz)j + (3xz² − y)k…

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Q: Find the solution. (D2+4D+4)y=0; when x =0, y=1, y'=-1. Ay = (1 – x)e2r y = (2 + 3x)e- y = (1 +…

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Q: dy = y + Vx² + y² dr Find the general solution of x-

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Q: Find the general solution. 1. (D2 + 3D − 18)y = 0

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Q: rx dydx Vx2+y2 0.

A: We solve this double integration problem by substitution method as given below in solution

Q: y = x + C,e* + C,e-2*

A: y=x+C1ex+C2e-2x

Q: d?y 13 으18 + t6/3- t2 + 246 3 Find if y(t) - dt2 3

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Q: y = t2 + 3, t = 3x? , z = Vx, find dz

A: Given that, y=t2+3  ;  t=3x2  ;  x=x We have to find dydz. Now we get, y=t2+3=3x22+3=9x4+3…

Q: What is the general solution of the equation y '(t) = 3y - 12?

A: We first separate the variables

Q: The solution of (D² – 4D+13)y 0 5 2x (A eix . Be Jox (A ex + Be)

A: D2-4D+13y=0 The auxiliary equation is m2-4m+13=0 ⇒m=4±-42-4132⇒m=2±3i

Q: (t+2)y"-y'-(4t+10)y=0 Given y1=e-2t Find y2?

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Q: Find the solution to xy' +y =x² + 1

A: To solve the given differential equations ,  After some steps , it is converted into linear…

Q: What could be the potential equation ? y² = 2? + x? a. 4y = z2 +x? C. z? = y? + x² %3D d. x² = y2 +…

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Q: f(7,y) = 8z² + 5y² + 4z'y+e7=y %3D Calculate 710

A: The given function is

Q: Obtain the genral solution. (D3 + 5D2 + 7D+ 3)y=0

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Q: find the Solution o f dy -2y-2

A: We are given the differential equation: dydx=2y-2 ⇒dydx=2y2⇒y2dy=2 dxNow Integrating both…

Q: Q2: solve the equation dx 2x dy y y 3.

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Q: Find the values of r for which y = e"* satisfies the equation y +2y -8y=0

A: The given differential equation is: y''+2y'-8y=0

Q: Find a constant solution of y′ = t2y - 5t2.

A: we have to find a constant solution of  y'=t2y-5t2

Q: Q4/Find x and y that make the equations equal to zero: 5x+2y-4=0 6x+8y-2=0

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Q: Find the solution of dy r(1+ y?) dr 4+22

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Q: Solve the IVP Cost y +7Y y(T) = 0, t> 0 %3D t2

A: Given IVP is,  y'+2ty=costt2, yπ=0, t>0.   It is of the form of y'+Pty=Qt. Here, Pt=2t and…

Q: Solve y′ = t − 5ty using both separable and linear methods, and verify that your answers are the…

A: Given data:   The given differential equation is: y’=t-5ty.     The given differential equation can…

Q: Find the solution for: y' – x e = 0 using separation of variables.

A: Solution of differential equation

Q: Q3) If y² + xy = 1, find y" at the point (0, -1)

A: We will differentiate twice and find the value of y" and it will be equal to,   - 1/4      The…

Q: The equation æ? + y² – z² = 1 in R³ describes %3D

A: Find your answer below

Q: Solve for the solution for the equation: y' + xy = 6x/y with the condition of y(3) = 6.

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Q: Find the solution of y − y = e2x , y(0) = 1.

A: Substitute value of the variable given in the equation. Then after calculation the value of other…

Q: Find the DE by eliminating the arbitrary constants |.cʻy² = xCx- )° %3D

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Q: Determine the solution to the I.V.P. y"+7y'+12y=2le",y(0)=,,y'(0)=-10 %3D vious Next

A: Please find attachment for the details solution

Q: Find the solution of the dy Qoec() +y d'ifferential equation.

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Q: Q2\Using the variation of parameter , find the solution of: y'+9y= sec3x

A: Particular solution by variation of parameter where W is wronskian of y1 and y2.

Q: y" – 6y' + 9y = :

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Q: Solve the IVP: y" + y = 6(t – 2m), y(0) = 0, y (0) = 1.

A: y“+y=δt-2π

Q: Is the equation y '(t) = 2y - t separable?

A: Given a differential equation, y't=2y-t

Q: a) Find the general solution of the equation d'y dy dr? + 3e* dr by using the method of undetermined…

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Q: Find Y in terms of x and y. d2y

A: Given an equation in terms of y and x as shown belowWe need to differentiate it with respect to x…

Q: Solve the he (D’+ 4D+4)y(x) = 5e equation y,)-(2x+1)e - y,) (2x+1)e y,(x) (2x-1)e 32

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Q: y"- 5y + 4y ez.

A: Use second order ordinary differential equation rules

Q: Solve : -4t y +2y -J ydt = e s(t-3) yco) = 0 ,y'co)= o y'co) =

A: Convert the given equation in Laplace domain: s2Y+2sY-Ys=e-34+ss3+2s2-1Y=se-34+sY=se-34+ss3+2s2-1

Q: y" – 2y' + y = e*/x

A: The given differential equation is…

Q: Solve the equation: y" -y = 2* + Oy=ce to xe +e* (x+c3e2X + CA) Oy=c₁e* + c₂e* + ex (x + c3e-²x +…

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Q: Use graphical methods to find two solutions to thesystem

A: Graphical method: The point at which graphof two equations intersect is the solution of both the…

Q: Is the equation t²y' (1) t + 4 - separable? y?

A: t2y't=t+4y2

Q: Find the general Solution of DES 2x y Y' = x? +2y} %3D

A: SOLUTION-

Q: Ex3) show That y= ē" is Solution Lor y+y`-2y=o

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Q: (x = s² – t² y = s·t³ z = 2x – 5y,

A: See the attachment

Q: Use the substitution z = y^2+ t −1 to solve 2yy′= y^2+ t −1

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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.