Form the differential equation for the function 2xy asin2x-bcos2x O a xy" -2y = -4y Ob.xy" + 2y= -4xy Oc xy" + 2y = 4y Od xy" -2y= 4y +2y=-4xy

Q: Solve the differential equation subject to the indicated initial conditions. y" – 2 y' + 5 y = 1+t,…

A: Given differential equation is y''−2y'+5y=1+t and y0=0, y'0=4 We have to solve the given initial…

Q: y = (C₁ + C₂x) eª + sinx+x²; y" - 2y' + y = −2 cos x + x² − 4x + 2

A: Here we find the first and second derivatives of given solution and then put in the left hand side…

Q: Show that the differential equation  (2xy3 - 3y2 + 2xy2)dx + (3x2y2 - 6xy + 2x2y)dy = 0 is exact and…

A: To show that the differential equation  2xy3-3y2+2xy2dx+3x2y2-6xy+2x2ydy=0 is exact and to find its…

Q: 5. Cx sin y +x²y = Ay

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Q: What is the particular I solution of the differential equation (2x + y²) dx + 2xydy = 0 when x = 1…

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Q: from the partial differential equation by eliminating the arbitrary function z=(x2+y2+z2)

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Q: Convert the differential equation x by letting u₁ = x, U₂ = x', Uz = x Note: Type u_1, u_2, u_3, and…

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Q: b Show that y = e' sinx %3D satisfies the differential equation (1 - x²)y" – xy' - y = 0. |

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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: Form the differential equation whose primitive is given by y= ex(a cos⁡x + b sin⁡x),  a, b, being…

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Q: What is of the differential equation (3 +y+ 2y sin² æ) dx + (x + 2xy – ysin2x) dy = 0 ? O 2x sin 2x…

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Q: Find the differential equation arising from o (x+ y + z, x² + y² + z²) = 0.

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Q: (4) Form the differential equation by eliminating the arbitrary constants a and b from y = a sin x…

A: Eliminating arbitrary constants a & b using derivatives.

Q: Determine the solution of the differential equation d5x ,d*x d3x d2x + 12 + 8 - ds5 ds4 ds3 ds2 а. x…

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Q: Determine whether the differential equation is separable. y'= 4x cos (y)-xy Separable Not separable

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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: 1. Form the differential equation by eliminating the constant A and B from y = emx (A cos nx + B sin…

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Q: SHOW THAT THE DIFFERENTIAL EQUATION IS LINEAR EQUATION OF ORDER ONE 2. (y – 2)dx + (3x – y) dy =&

A: We can solve this problem as follows:

Q: Form a differential equation from the given function. y = Asin(2x)-5cos(2x)

A: Giveny=Asin(2x)-5cos(2x)   ----{1}

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

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Q: Form a differential equation by eliminating arbitrary Function. Z= (x + y)f(x² + y² ) %3D

A: Given z = (x+y)f(x2+y2)zx+y = f(x2+y2)                             (1) Partially differentiate with…

Q: Write the differential equation y"+ 5y +y=0 in standard form: y"+ y'+ y = 0 ngular points of the…

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Q: a differential equation is classified as a homogeneous DE if one can directly isolate all functions…

A: A differential equation is classified as a homogeneous DE if one can directly isolate all functions…

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: Form the differential equation for the function x+2y=a sin3x-bcos3x

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Q: The given differential equation is already in standard form, as the coefficient of the highest order…

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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 4y"- siny y' + 3y = O is a linear equation. :Select one True False

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Q: a) Find the differential equation of X ae(2+last digit of your id)y + %3D be-(2+last digit of your…

A: Consider the provided question, Given, last digit of id is 9. Substitute this value in the given…

Q: Obtain the differential equation of all straight lines with alebraic sum of the intercepts fixed as…

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Q: Find the differential equation by eliminating arbitrary constants "A" and "B" from the family of…

A: The given family of curves                    y=Acos12x+Bsin12x , where A and B are constants.

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

A: In this question, we have to find the differential equation by eliminating parameters.

Q: Verify that the general condition satisfies the differential equation. Then find the solution that…

A: y''+9y=0 is the given DE with the general solution y=C1sin(3x)+C2cos(3x)...(1) To verify the general…

Q: Obtain Differential Equation by Substitution:  DE dv/du=(u-v)^(2) -2 (u-v)-2

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Q: Form the partial differential equation by eliminating arbitrary function from z = e" f(x – y)

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Q: Use the initial condition to find the particular solution of the differential equation. Differential…

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Q: Find a differential equation of the family of cubics cy² = x² (x – a) with 'a' held fixed.

A: The given expression is,  Assume 'c' as the arbitrary constant and 'a' as a parameter. Take log on…

Q: The solution of the differential equation (xy – y²)dx – (x² + y²)dy = 0 is : %3D A) 2 In + 1| – In |…

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Q: Determine the differential equation of the family of lines passing through the origin O ædx + ydy =…

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Q: Determine the differential equation whose general equation is 1. y = Ce-2x + C,e3x 2. y = Ce* +…

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Q: Form the partial differential equation by eliminating the arbitrary constants a and b from z = ď² x…

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

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Q: Form the differential equation for the function 2x-y = asin(2x - b) O a. y" + 4y = 8x O b. y" +y = x…

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Q: soWE THE DIFFERENTAL FQNATUON Zydx-(3xy°dx - xdy =0) %3D when x= 2 ,y=2

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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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Q: Form the differential equation if its solution is y=acos2x+bsin2x a. y"+4y=0 b. y" – 4y = 0 c.…

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Q: Obtain the Differential Equation from the given general solution. y = C¡ cos(4x) + Cz sin(4x) + Cx…

A: Use the following formula, to find the solution. ddxcosax=-asinaxddxsinax=acosaxddxuv=udvdx+vdudx

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.