Find the particular solution that satisfies the differential equation F'(X) = 10x − 12x3 with an initial condition of f(3) = 2

Q: У"(х) — 2у(х) + у (x) — 4x2 — 3 + et

A: Given :         y''(x) - 2y'(x) + y(x) = 4x2 - 3 + exx   To find:            The general solution of…

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

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Q: ху xy' = y(1+ln2)

A: The given differential equation is  xdydx=y1+lnyx

Q: By using substitution of x-e' and t = ln(x), find the general solution of the differential equation.

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Q: Create a third order, non-linear Ordinary Differential Equation with enough initial values to be…

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

A: To solve:

Q: Find the general solution of the first order differential equation (x+2) y′ + 4y = (3x + 6)-2 lnx.

A: Given: x+2y'+4y=3x+6-2lnx for finding solution of given differential equation, first we convert it…

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

A: f(x)=∫f'(x) dxf(x)=∫(16x3-6x)dxf(x)=16x44-6x22+C              (∫xndx=xn+1n+1)f(x)=4x4-3x2+C where…

Q: Find the value of the arbitrary constant of the particular solution of the differential equation…

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

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Q: Find the differential equation by eliminating arbitrary constant  y=Ae-3x+Be2x

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Q: Find the differential equation associated with y = clx^2+ c2x + c3

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Q: Obtain the solution of the differential equation y′ = (x + y)^2

A: Given differential equation is: dydx=(x+y)2                       (1) Let us assume (x+y)=t…

Q: What is the appropriate method to find the general solution of this differential equation?

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

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Q: 4. (D* – 1)y = 0

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Q: Find the solution of the differential equation that satisfies the given initial condition. dP

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Q: -3-x+x. y (0) -2. y(0)

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Q: Find the particular solution of the differential equation - ytanx e" secx that satisfies the initial…

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Q: Solve for the general solution of the given first-ordered Linear Differential Equation udx + (1 —…

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Q: 2x + 2xy2 y + 2x²y dy dx ||

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Q: If μ(x) is an integrating factor for the differential equation (x+2)y∗(x−2)y=8x. then…

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Q: the given differential equation is not exact and hence show that Solve it x²ydx -lx3+y?)dy=0

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Q: Use separation of variables to find the general solution of the differential equation. (6 + x)y' =…

A: Please refer the attached image for complete solution.

Q: Find the general solution of the differential equation 2xyy' = 2y² – x²

A: given 2xy y' = 2y' -x'y' = 2y2-x22xy---(1)put y =vxy' = v + xv'---(2)so from (!) we have y' =…

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

A: Since you have asked multiple questions, we  will solve the first question for you. If you want any…

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

A: Given that f'(x) = 20x3 - 8x and f(1) = 1 then find particular solution. Here i attached solution of…

Q: Find the general solution of the differential equation with clear steps.

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Q: (D4 - 1)y = 7x².

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Q: Find the particular solution to the differential equation y'=2x passing through the point (2,7)

A: given differential equation is y'=2x we can write it as dydx=2xdy=2xdxy=x2+c

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

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Q: Use separation of variables to find the general solution of the differential equation. (9 + x)y' =…

A: We have,

Q: 2) (x²y³ + y)dx + (x³y² – x)dy = o

A: (x2y3+y)dx+(x3y2-x)dy=0 this is an exact equation  M(x, y)= x2y3+y N(x, y) = x3y2-x We will evaluate…

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

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

A: To find The particular solution that satisfies the differential equation and the initial condition.

Q: Find the particular solution that satisfies the differential equation and initial condition. - 7…

A: Given query is to solve the differential equation and find the function f(x).

Q: Solve the differential equations using method of undetermined coefficient y"+y = x^2sin(2x)

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Q: xy'= y + 2x'

A: xy' = y + 2x3xy'-y = 2x3Dividing by x;y' -1xy = 2x2 ...(1)Comparing with Bernouli's equation;y'+P(x)…

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: 3. (D² + 4)y = 0

A: Given:         D2+4y=0      Auxiliary equation is        m2+4=0         m2=-4          m=±-4…

Q: Find the general solution of the differential equation using any method         y′ = ln(x2 + x)

A: we have to find the solution of the given differential equation  y′ = ln(x2 + x)

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

A: Given that: f'x=x3-9x2;     f2=9

Q: Find the differential equation whose complete solution is y=c1e-x+c2ex+4x using elimination of…

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Q: Find the solution of this higher order differential equation

A: Given that: (D4-3D3+4D)x=6+80cos2y

Q: Use separation of variables to find the general solution of the differential equation. (5 + x)y' =…

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Q: y' = ycotx + y²cscx

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Q: Find the particular solution to the differential equation y′ = 4x + 3 passing through the point…

A: To find: y'=4x+3dydx-4x=3       dydx+Py=Qwhere P and Q are variables of x onlyI.F.(Integrating…

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

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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.