Evaluate the Particular solution of the differential equation and find x when y = 0. If decimals, use 8 decimal places. 2x[3x + y - y exp(-x²)]dx + [x² + 3y² + exp(-x²)]dy = 0 IC:x = 0, y = 1

Q: Find the particular solution of the differential equation that satisfies the initial conditions.

A: The given differential equation is in variable separable form. Hence, an be solved using simple…

Q: Given that y = e^x is a solution of (x - 1)y" - (x + 1)y' + 2y = 0, find a linearly independent…

A: The solution is given as

Q: verify that the function y=e^-4x is a solution to the differential equation y'' + y' - 6y =0

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Q: Solve the differential equation d'y dy +4 = e-3x %3D dx dx by using the method of variation of…

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Q: Calculate the value(s) of C for which y=x'-2C is a solution to the differential equation dy -3y-54 =…

A: We have to find the value of C

Q: Determine whether the function y = 2 sin 2x is a solution of the differential equation y"-8y = 0.

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Q: i. Solve the differential equation (x + dx-y = (x+2)², given that when x = 0, y = -4.

A: This is first order ordinary non homogeneous differential equation.

Q: Find the particular solution of the differential equation given that, when x = 0, y =-4 and Q3 *…

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Q: Solve the general solution of the given differential equation by making it exact. 1.)(3xy +y' )+(x°…

A: Put y=vx and solve. ∫1ax+bdx= 1aln(ax+b)+C Note: According to Bartleby Guidelines , we can solve…

Q: Find the general solution to the differential equation for x(t), x" – x' – 2x = 4e¬2t + 9e2t.

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Q: Solve the given differential equation by undetermined coefficients. y"+ y' + y = x2 - 3x 4 y(x) =

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Q: Verify that the function y = e-3x is a solution to the differential equation d2ydx2 + dydx − 6y = 0.

A: We have to verify the solution

Q: Determine the solution y2(5) of the differential equation, given that it is satisfied by the…

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Q: Solve the given differential equation by variation of parameters. x²y" + xy' – y = In(x) y(x) = ,x >…

A: Given: The equation given is x2y''+xy'-y=ln(x). Assume y=xr be the solution. Differentiate the…

Q: Solve the differential equation  (1+e2x)dy + (1+y2)dx=0 ,given that y=1 at x=0.

A: Given- 1+y2dx+1+e2xdy=0 To find- The solution of the above differential equation at 1,0. Concept…

Q: Solve the given differential equation by using an appropriate substitution. The DE is homogeneous.…

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Q: Determine if the differential equation (3x2y + ey)dx +(x3 + xey - 2y)dy = 0 is or is not exact; if…

A: Given problem:- Determine if the differential equation (3x2 y + ey )dx +(x3 + xey - 2y)dy = 0 is or…

Q: Solve the given differential equation by separation of variables. dy - xy + 3x - y - 3 dx xy - 4x +…

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Q: Find the general solution of the given differential equation, and use it to determine how solutions…

A: The general solution will be the sum of the complementary solution and particular solution.   The…

Q: Solve for the particular solution of the differential equation 2xy dy/dx = x 2 + y2 with the given…

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Q: Determine whether the function y = ln x + e2x + Cx4 is a solution of the differential equation y(4)…

A: Given differential equation is y(4)-16y=0 Given function is y=lnx+e2x+cx4 Differentiate y repeatedly…

Q: Evaluate the Particular solution of the differential equation and find y when a = O and x = 2. If…

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Q: Determine whether given differential equation is exact. If it is, find the solution. 3y (x² – 1) dx…

A: Let's find.

Q: Solve the general solution of the given differential equation by making it exact. 2.)y?dx + (xy-1)dy…

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Q: solve the first order homogenous differential equation (x² + æy) dy = (æ² + y²) dæl

A: The differential equation is given as x2+xydy = x2+y2dx It can be rewritten as dydx = x2+y2x2+xy…

Q: Find the general solution of the given differential equation. (x + 1) dy + (x + 2)y = 2xe-x dx 11

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Q: Find the particular solution to the given differential equation that satisfies the given conditions.…

A: Given differential equation is:  d2ydx2-2dydx+y=e-4x(x-1);     y'(0)=0, y(0)=0 Solution of…

Q: Find the general solution for the differential equation: (2xy²-2y)dx+(3x²y-4x)dy=0

A: Given :(2xy2-2y)dx+(3x2y-4x)dy=0

Q: y"-2y'+5y = e"sinx

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Q: Find a particular solution to the differential equation using the Method of Undetermined…

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Q: dy -x² + y² = xy + y? = xy ху dx

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Q: Solve the given differential equation by undetermined coefficients. y" + 2y = 2x + 3-e-2x y(x) =

A: Follow the procedure given below.

Q: Solve the given differential equation by using an appropriate substitution. (x² + y²)dx + (x² +…

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Q: Solve the given differential equation by undetermined coefficients. y" – y' – 12y = e4x %3D y(x)

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Q: Specifically a differential equations problem. Question in pic below.

A: We are given the differential equation,                                   First, we will solve the…

Q: Verify that the differential equation is homogenous, then solve it by substitution: (4x-y) dx +…

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Q: x*y" - 2xy' +2y = In x |

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Q: Determine the solution y2(5) of the differential equation, given that it is satisfied by the…

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Q: Find the general solution of the given differential equation. x²y' + xy = 2 y(x)%3D

A: This is a problem related to differential equation. Based on the general formula we will answer the…

Q: Find the general solution of the given differential equation, and use it to determine how solutions…

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Q: Find a particular solution to the differential equation using the Method of Undetermined…

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Q: Find the general solution of the differential equation. (Use C for any needed constant.) dy = 10 - Y…

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Q: Find the particular solution to the differential equation d?y = 4e* + 3x² dx2 dy given y = -3 and dx…

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Q: Find the general solution of the given differential equation, and use it to determine how solutions…

A: Given differential equation is,

Q: Find the general solution of the differential equation. (Use C for any needed constant.) (dx)/(dy) =…

A: dxdy=10-y Formula ∫adx=ax+C∫xndx=xn+1n+1+C

Q: Find the particular solution for the differential equation: y''+2y' +y = (x^2)(e^-x)

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Q: y²dx + (xy – 1)dy = 0

A: First of we will check whether given DE is exact or not

Q: dx x2-y2-xy 0 ху dy

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Q: Determine the solution of the given differential equation: (x² – xy + y²)dx – xydy = 0 ; when y (2)…

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