(2y-1 + cos 3z) 분. 4x3 + 3y sin 3x = 0 (1)

Q: An Integration factor of this differential equation is .7 3x? + 1 + x3 dy 1 y : 1+ x2 dx

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Q: 3) yy +x²(sinx)³ = y³cotx %3D

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Q: first-order

A: Given : y' = x9y + sin(x) The standard form of first order differential equation is  y' + p(x)*y =…

Q: What is the general solution of the differential equation y" +4y= tan 2x? Oy C1 cos 2x + C2 sin 2a -…

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Q: Obtain the differential equation of the family of circles with center at point (h,k) and radius r.…

A: The equation of the circle having a center (h, K) and radius and radius r is given by:…

Q: Find a homogeneous linear differential equation wit Gcosh 2x coc E 2x cin 5

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Q: 4. Show that both x₁ (t) = et cost and x2(t) = et sint are solutions to the second-order…

A: To show that both x1t=e-t cos t, and  x2t=e-t sin tare solutions to the second‐order differential…

Q: Use integration to find a general solution of the differential equation             dy/dx = ex/(4 +…

A: Given ,           dydx=ex4+ex

Q: Suppose !=sinh2r, z= 6ư, 3s= cos2r are solutions of a linear homogeneous differential equation with…

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Q: The order of the differential equation of all circles of given radius a is: 3 2

A: Let's find.

Q: Find the differential equation of the families of circles with center at (2, k) and with radius r.

A: Given,           The differential equation of the families of circles with center ar 2,k and with…

Q: (3nny-5x)dx+ 2x*cotydy = 0

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Q: Find the differential equation of the family of circles of fixed radius r with center on the x-axis.

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Q: Find the differential equation of all sphere of radius 5 having their centers in the xy plane

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Q: Find the Differential equation by eliminating the arbitrary constant from the given  y = Acos3x +…

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Q: Find general solutions of the differential equation    (2xsinycosy)y'=4x^2+sin^2 y

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Q: Obtain the differential equation for the family of circles with center on the line x = 8.

A: The general equation for a circle can be written as

Q: a. Circle of radius 1 and centers on the line y = x

A: The solution is given as

Q: USE EXACT DIFFERENTIAL EQUATIONS To SOLUE THE $OLLOWING: In dx-tn(x=2) 'पर्क - डेण बर =0 y dy dx 3D0…

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Q: Form a differential equation from y = 3cx - 4, here c is the arbitrary constant.

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Q: The differential equation ry" + 3y - 7y=seca is normal on any open interval not containing a = 0.…

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Q: Which óf thé fóllówing directión fiéld will represent the differential equation y' = y + 1 Option 1…

A: Direction field: A graphical representation of solutions of a first order differential equation is…

Q: 1. (2x + y – 1)dy + (4x + 2y – 3)dx = 0; when x = 1, y = 2

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Q: Find the differential equation of the family of cuves and draw at least three members of the family…

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Q: (2 + tan2x)(1+е"У)dx — е У tan x dy %3D 0 = 0 %3D

A: Given differential equation is 2+tan2x1+e-ydx - e-ytan x dy = 0,   yπ2=0

Q: The integrating factor of the linear first order differential equation dy dx sin2x- y+tanx Oa None…

A: The standard formula for the linear differential equation is dydx+P(x)y=Q(x). Here, P(x), Q(x) are…

Q: 4. y" +2y'+ = cos a COS

A: We will solve the problem

Q: What is the auxiliary equation associated with the second order linear differential equationd^2x…

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Q: -) Solve the following partial differential equation us ing direct integration: a²u = cos (x +y) дх…

A: Topic:- application of integration

Q: What is the order of the lowest order homogeneous differential equation which has a particular…

A: Given particular solution y=x2+exsinx2 We have to find the order of the lowest order homogeneous…

Q: 3. ydx+(1+x)arctanx dy= 0

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Q: 2. dx + 2x dy/y 2x2 y2 dy

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Q: 4. y" + 4y = sin² 2x when y () = 0; y' ( = %3D

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Q: (3tanx-2cosy)sec²xdx

A: We will solve the differential equation.

Q: Find the differential equation of all family of straight lines at a fixed distance p from the…

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

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Q: 2. y" + 4y' + 5y = cos(x)

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Q: Show that (2x cos y + z siny) dx + (xz cos y – x² siny) dy + x siny dz is an exact differential.…

A: Given differential equation,2x cos y z sin y dx + xz cos y -x2 siny dy + x sin y dz =0

Q: The solution of the first order linear differential equation y' + ycotx = cosx is O…

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

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Q: Obtain the differential equation of all circles with center on line y = -x and passing through the…

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Q: These equation classifies by dy 3 +5x y dx' tan x dx Ordinary Differential Equation O Partial…

A: By see tha solution of this question

Q: الموافق Find the general integra) of the differential equations with dottedf v ariables : ト 3) (++y)…

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Q: Find the differential equation of all sphere of radius 5 having their centers in the xy planes

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Q: (1+ cosx)y' = sinx(sinx + sinxcosx – y) |

A: 1+cosxy'=sinxsinx+sinx cosx-y On simplification, we get ⇒1+cosxy'=sin2x+sin2x…

Q: Transform into first order linear form the differential equation sin 0 dr 2rcos0 %3D OP

A: First order linear form of the differential equation is:  drdθ+P(θ)·r = Q(θ) hare P(θ), Q(θ) are…

Q: 9. Use separation of variables to find the general solution of the differential equation. dy = sinx

A: y2 dydx=sinx sperate the variables y2 dy=sinxdx

Q: azu Ex: Solve the partial differential equation дудх sin³x cos²y given that du %3D siny when x=0 and…

A: First take x as a constant and integrate with respect to y and the other one

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