The differential equation formed by eliminating arbitrary constants a ,b andc: y = ax + bx + cx + 8 is

Q: show that function  y1=x-1 is a special solution of the differential equation y'=1 - ( y-x+1)2 and…

A: Given the differential equation y’ = 1 – ( y – x + 1)2 and we have to show that y  = x -1 is a…

Q: 5x y = C, + C2e4x 4

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Q: Show that the first order differential equation (x + 1) y' - 3y = (x + 1)5 is of the linear type.…

A: To solve x+1y'-3y=x+15; y=1.5 when x=0

Q: Help

A: In such problems ie second order linear differential equations when we are given one solution,y1 we…

Q: Use separation of variables to find the general solution of the differential equation. x2 + 6yOy = 0…

A: Given query is to find solution of the differential equation provided.

Q: y + 3xy' – 2(y')³ = 0

A: Product rule of differentiation: (fg)'=fg'+gf' Chain rule of differentiation:…

Q: dy y3 dx x3 + xy² II

A: Given: - The differential equation is, dydx=y3x3+xy2 To show: - The given differential equation is…

Q: (3ху2 — у?)dx + (2х?у - 2у)dy - 0

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Q: solve the for the general solution of the differential equation( linear homologous equation): (D2 +…

A: We have to solve the differential equation: D2+2D-1y=0 The given equation is in symbolic form where,…

Q: Let y' (x) = V1– y²(x) be a differential equation. What is a solution?

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Q: 0 = 2e³i – e2', do - + 30 = -2e²' dt - dr?

A: To determine whether the given function is a solution to the given differential equation.θ=2e3t-e2t,…

Q: az = 0 ду 4(z, 0) = 4 · e-z

A: To solve a differential equation using  variable separable or dividing the variable   Assume the…

Q: Solve the differential equations using the substitution suggested by the equation. (x + 2y - 1)dx +…

A: Given the differential equation is (x + 2y - 1) dx + (2x + 4y - 3) dy = 0; when x = 2 and y = -1.

Q: Show that the function  y1=x-1 is a special solution of the differential equation y'=1-(y-x+1)2 and…

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Q: Solve differential equation, subject to the given initial condition.

A: This is a first order differential equation. This can be solved using the integrating factor method.…

Q: Find the differential equation that has y = C1 + C2x as its general solution.

A: To find the original differential equation we  have to eleminate the arbitrary constants by…

Q: Obtain the differential equations satisfied by the given puiiicular 3. y = e5x - 3x - x2 4. y = e3x…

A: According to our guidelines we can answer only three subparts, or first question and rest can be…

Q: Find the particular solution to the differential equation: 2(y')² ( y" = 1- when +3) x = 0, y = 1…

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Q: Find the differential equation whose general solution is y = C1x + C2ex. %3D

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Q: Find the particular solution that satisfies the differential equation and the initial condition. x²…

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Q: Solve the differential equation by variation of parameters, subject to the initial conditions y(0) =…

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Q: Now find the solution of the differential equation that satisfies the conditions y(0) = 4 and y' (0)…

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Q: Form the differential equation by eliminating the arbitrary constant A, B from y=Ae?x+Be7*

A: We have to form differential equations

Q: The independent variable x is missing in the given differential equation. Proceed as in Example 2…

A: Given:y+8yιι =yι2   →1Let yι =u →Ad2ydx2=dydxd2ydx2=dudy=dydxd2ydx2= ududy →Busing Aand B in 1we…

Q: Find the particular solution to the differential equation when y(0)=3 and (2)=1

A: Given differential equation isy''=y'2x-y'x2-1 The conditions are y(0)=3,  y'(2)=1

Q: form the differential equation corresponding to (y – b) = 4(x -a) %3D

A: Given: The equation is (y-b)2=4(x-a)   To determine: The differential equation from the equation…

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

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Q: y² = Ax² + B sec x

A: Given equation: y2=Ax2+BsecxTo find: General solution by eliminating all the arbitrary…

Q: The differential equation obtained by eliminating the arbitrary constants A and B from the relation…

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Q: Find a homogeneous linear differential equation with constant coefficients whose general solution is…

A: We have given the general solution y = C1 + C2e2xcos 5x +  C3e2xsin 5x

Q: Solve the differential equation by variation of parameters, subject to the initial conditions y(0) =…

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Q: Show that the differential equation dy -2 - yezy dr rezy – 2y is exact and find its solution. 3.

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

A: y'' +3y' +2y=12+exA second order linear, non-homogeneous ODE has the form of   ay''+by'+cy=gxThe…

Q: Find a differential equation whose general solution is 9t = C₁e⁹t + c₂e-5t. y = = 0

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Q: Find the general solution of the differential equation: y" – 2y - 3y= - 3te. Fi: of the…

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

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Q: Give the detailed solution of this differential equation using 1st order and 2nd order 1. (y') ² +…

A: This is a problem of differential equation.

Q: A solution for the differential equation is y = Pe-3x/2 + Qe–x/2, %3D

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Q: Find the general solution of the differential equation or state that the differential equation is…

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Q: Find the general solution of the differential equation. Use C, C1, C2,⋅ ⋅ ⋅to denote arbitrary…

A: Consider the given differential equation as v"x=5x2

Q: Solve the differential equation by variation of parameters, subject to the initial conditions.…

A: The given differential equation is 2y''+y'-y=x+7 and the initial conditions are y0=1, y'0=0. The…

Q: The complementary solution for following differential equation d3x + 5 d2x +26 dt2 dx dt3 150х 600t…

A: In the question it is asked to calculate the complementary solution of the function given below.…

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

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Q: = Form the differential equation by eliminating arbitrary constants : y = ax +0x , .3

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Q: Solve the differential equation for y= y(x) if y+2ry + 2x = 2 + 2y given the initial condition that

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Q: Find the general solution of the differential equation or state that the differential equation is…

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Q: Show that the differential equation x¹y³ + x(1+y¹)y' = 0 is not exact, but becomes exact when…

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Q: The differential equation (2x' - xy - 2y+3 dx- (x²y+2xdy = 0 is exact because OM ON

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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.