Solve the DE. If o(x) is the solution to the DE, find o( - 2) $( – y = xe- x*: (0) = 0

Q: 2. Find the general solution of Ei-0 (2)*y(n-1) = 0. %3D

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Q: Solve the equation using Exponential Shift (D² - 2D + 2) y = 12x³e²x O y = e (c! COSx + c2 sinx) +…

A: Answer is given.

Q: Find 2 and z if z is defined implicitly by the equation ду x² + 2xyz + y° + e² = ln 4

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Q: The solution of the ODE * dy_ (x² + y²) || dx x2

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Q: If y = x2 – 2x and x changes from 2 to 2.01, find ∆y. (SOLVE BY USING DIFFERENTIAL EQUATIONS)

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Q: 2) Determine the constant A such that the equation (x² + 12ry) dx – (Ar² + 8y) dy = 0 is exact and…

A: The differential equation P(x,y)dx+ Q(x,y)dy =0 is an exact equation if and only if…

Q: (ax-3 (x+4)8 Degreez co EGAelents

A: The detailed solution is given below Thank you

Q: Solve differential equation  (D3+2D2+D)y=x3

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Q: Find the General Solution of (D² + 5DD' +6D2)Z = 10 cos(x - y)

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Q: The differential equation d5y d³y 4x- + 5y=e* – cos2x in D-notation is dx5 dr3

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Q: 1. 3(3x² + y²)dx – 2xydy = 0 -

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Q: Xy = ý+2xy is DE, solve it:

A: ..............(1)

Q: Using an operator , solve the following differential equations d2y/dx2- 10dy/dx + 25y= 0

A: This question is based on solution of differential equation using D operator.

Q: z = xy dy x2+y= 2x/1-x’y² dx 2. Using the substitution ,change the to a separable equation. Hence…

A: We are given the differential equation  xdydx+y=2x1-x2y2 we have to use the substitution z=xy.

Q: Determine the appropriate form for a particular solution of the fifth-order equation(D - 2)3 (D2 +…

A: Given differential equation is D−23D2+92y=x2e2x+xsin3x......1. We have to determine the appropriate…

Q: If f(x)=Aekx , f(0) = 5 and f(3) = 10, find k. (SOLVE BY USING DIFFERENTIAL EQUATIONS

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Q: 3. Find the general solutions of, x+y dx x-y, a.

A: We have to solve the given differential equation.

Q: solve the equation by using Bernoulli's equations. y' + p(x)y = f(x) y ln y

A: Y’ +p(x)y =f(x)ylny divide equation with y both side we get y’ /y +p(x) = f(x) lny now consider lny…

Q: Determine the form of a particular solution y, (x) for y" - 4y'+5y e*+xsin 3x- cos 3x. [Do not…

A: Solution: The given differential equation is y''-4y'+5y=e5x+x sin3x-cos3x. For the complimentary…

Q: 3x (b) Find the general solution of +2y=e*

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Q: 2 cos(2x) = -V3 a)

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Q: 3) a) Solve:' 4x³y +4x?y(2)_ sxy'+2y=0 Co,0) on

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Q: L" + 2x" – x' – 2x = et Write the equation as a 1st order linear differential equation system and…

A: Given equation is  x'''+2x''-x'-2x=e3t                                                (i) Let…

Q: Example: Find the general solution of the equation a²z = e2x+3y + sin(x- 2y), H.W. +2 дхду

A: Given partial differential equation is ∂2z∂x2−3∂2z∂x∂y+2∂2z∂y2=e2x+3y+sinx−2y......1. We have to…

Q: solution of the di dy x + 4y = * x2

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Q: Test the DE for exactness then solve. 5. (3x2 + e2y)dx + (2x e2y – 4y)dy = 0

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Q: Find an integrating factor and solve the equation 4x y' = e¹x + 8y - 1.

A: Solution of given question is written in below steps.

Q: x2 dy dx2 d²y dy + 2y = 5x° cos(x) 2x Jx - dr solve the equation by undetermined coefficients method

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Q: 3. Find the constant a so that o(x) = re2 is a solution to y+ay- e =0. 0 4 O 3 0 1

A: ϕ(x)=xe2x is a solution to y'+ay-e2x=0

Q: d²N Solve t di? dN - 2t- dt + 2N = t In t

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Q: (x² -2x9 dy Solve The firest orler oDe

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Q: e solution of the di: 0.1 with step size 0

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Q: Solve the nonhomogeneous ODE. x²y" – 6xy' + 6y = x'e-3* %3D

A: We will first find the homogeneous solution. Then we will find the particular solution using the…

Q: dv Solve ax + by + c dx

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Q: e

A: We are given the following differential equation: 1+exydx+exy1-xydy=0 We have to find the general…

Q: Find the general solution of y' = y sec x

A: Given, The differential equation y'=ysecx We have to find the general solution.

Q: Non Homogeneous LDE solve: (D2  +  D  -  2)y  =  2x  -  40 cos 2x

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Q: Solve e (3x²y – x²)dx+ e*dy = 0

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Q: solve the IVP x2y"+5xy'-12y=0, y(1)=-1, y'(1)=-7

A: We can not solve if we substitute x=lnt , Because this is homogeneous differential equation or…

Q: 2 = 3x° (7 + y²) dx

A: Here equation is separable so w separate them and apply integration.

Q: 2. Determine the general solution to the equation y' + 2xy = e-2". %3D

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Q: Solve the Bernoulli equations x2y' + 2xy = y3

A: First, divide the whole equation x2y'+2xy=y3 by x2y3 to convert it into the form of…

Q: The solution of the ODE dy (x² + y²) dx x2

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Q: Find the general solution of D² + 16D)y = cos4x

A: We have to find general solution of the differential equation: D2+16Dy=cos4x Auxiliary equation…