Find the solution of the differential equation using Reduction of Order. (D² + 4)y = Sinx

Q: Solve the differential equations using the substitution suggested by the equation. (2x + y)dx -3(2x…

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Q: Give the general solution of the differential equations.   y" - y' - 6y = sin 2t

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Q: Solve the Differential Equation (D² + a²)y = Tanax by the method of Variation of Parameters.

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Q: Find the differential equation whose solution is given by: y^2=4ax

A: To find the differential equation for y2=4ax differentiating this equation with respect to x.

Q: .x = y + dy dr X2 - y²

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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. xy' + y = 20Vx

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Q: Find general solutions of the differential equation  2xyy'=x^2+2y^2

A: To solve:

Q: Find the particular solution of each differential equation that satisfies the initial condition.…

A: The given differential equation is: y'-8x3y=e2x4;       y(0)=2

Q: Determine the solution to the differential equation given by: y'=6y2/x

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Q: A solution for the differential equation is y = Pe-3x/2 + Qe-x/2.

A: Here P and Q are two Arbitary constant ,so the heighest order of the differential equation is 2.

Q: Find a differential equation whose general solution is y = c₁e³t+c₂e-2t 2 = 0

A: We need to determine a differential equation corresponding to the general solution: y=c1e5t+c2e-2t.

Q: -y'-11ly 0

A: Given differential equation is y''-y'-11y=0

Q: Solve the differential equation 1.) dy = (y²xe^3-3x²y)dx

A: Please see the below picture for detailed solution.

Q: Find general solutions of the differential equation      2x^2y-x^3y'=y^3

A: 2x2y-x3y'=y3 We need to find the general solutions of the differential equation.

Q: Determine the solution of the differential equation by separating the variable dy ,3x-2y + x²e-2y dx

A: given differential equation dydx=e3x-2y+x2e-2y claim- solve the differential equation by separating…

Q: find the solution of this differential equation: (x − 1)y′ = y + 2(x − 1)^3

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Q: Find general solutions of the differential equation    (x^2-1)y'+(x-1)y=1

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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: Find the general solution of the differential equation: 3ydx = (3x + 1)dy

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Q: Find general solutions of the differential equation    2xy+x^2y'=y^2

A: Given

Q: 2ydx = (x2 – 1)(dx – dy)

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Q: Formulate a differential equation that is satisfied by 1. y=Ae2+ Bxe²r

A: To find: The differential equation: Given: The equation is y=Ae2x+Bxe2x. Concept used: Product rule:…

Q: Find general solutions of the differential equation      y'=y+y^3

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Q: Find a differential equation whose general solution is y = c₁et + c₂e-4t . = 0

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Q: Determine the solution to the differential equation given by: y'' + 3y -10y= 0

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Q: Find general solutions of the differential equation          x^3+3y-xy'=0.

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Q: The general solution of the differential equation 2x(y + 1) dx — у dy is:

A: Given the differential equation: Now,

Q: 2) x – 1 = - 2e-y

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Q: Find the general or Special Solution to the differential equation 2 y = (x-y₁²

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Q: Solve for differential equation  (y2-xy)dx+x2dy=0

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Q: This is a differential equations problem.

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

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Q: Match the differential equation with its solution. y' - 4x'y = x3 %3D

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Q: Solve the differential equation. xy' + y = 7Vx

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Q: Solve the differential equation by variation of parameters. 9x y" - 9y = %3D 3x e y(x) =

A: The given differential equation is y"-9y=9xe3x.

Q: Find general solutions of the differential equation      2x^2y+x^3y'=1

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Q: Solve the Differential Equation using VARIATION OF PARAMETERS: y''-2y'+1=(x+1)e2x

A: The given differential equation is: y''-2y'+y=(x+1)e2x

Q: Solve the differential equation y2 − 3x dydx = 6.

A: follow the next step

Q: Find general solutions of the differential equation  x^3y'=x^2y-y^3

A: the given equation is x3y'=x2y-y3 divide the equation by x3 y'=1xy-1x3y3            ...... (1)…

Q: Find the general solution of the differential equation y2y′ = sin 9x

A: Given:          y2y'=sin 9x Where y'=dydx

Q: Find general solutions of the differential equation    (x+y)y'=1

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

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Q: Find general solutions of the differential equation    y'+3y =3x^2e^-3x

A: y'+3y=3x2e-3x Comparing with y'+Py=Q, we get P=3  &  Q=3x2e-3x Now integrating factor is,…

Q: Solve the differential equation by an appropriate method. y''+2y'=x^2+4e^2x

A: Given linear differential equations with constant coefficients. We have find General solution for…

Q: Find general solutions of the differential equation  (x^2-y^2)y'=2xy

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Q: solve the differential equation using the substitution method. (3siny-5x)dx+2x2cotydy=0

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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: Find general solutions of the differential equation        2xy'+y^3e^(-2x)=2xy

A: Rewrite the equation. Multiply the equation by 1/y 3 . Let 1/y 2 = t . Differentiate both sides…

Q: Find the solution of differential equation 4º+y = sin dx2

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