Solve the equation. (4x2 + 2x-1y)dx + (x²y° - 1)dy = 0

Q: Find the roots of the equation: d³ y 4. dx3 dy 13 — +бу dx -

A: 4d3ydx3-13dydx+6y=0we have to find the roots of the equation

Q: نقطتان What is the best way to solve this ?equation dy 4x2 + x %3D dx y + 4

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Q: Solve the following equation by separating the variables: (4y + yx²)dy – (2x + xy²)dx = 0

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Q: solve using bernoulli's equation 2xdy + y(y2lnx-1)dx = 0

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Q: Given that x- y2 = 9, then dy/dx =||

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Q: Determine whether the equation is exact. If it​ is, then solve it. (1/y)dx-(7y-(x/y2))dy=0

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Q: Solve the equation: (dy/dx) + (3y/x) + 2 = 3x, y(1) = 1. %3D

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Q: Determine whether the equation is exact. If it is exact, find the solution.  dy/dx=−(Ax−By)/(Bx−Cy)

A: Given differential equation is  dydx=-Ax-ByBx-Cy It can be written as…

Q: Rodrigues' Farmula (x²-1)! %3D 2L L! dx' Solve for Pg cx), P4 Cx), PEC

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Q: H.W. // Solve dy - 3y = x? dx

A: Given  dydx-3y =x2Given equation is of the form dydx+py = Qx   I.F = e∫pdx∴solution of differential…

Q: Solve an exact equation?  M(x,y) + N(x,y)*dy/dx = 0

A: Given: M(x,y)+N(x,y)(dydx)=0

Q: dy 2x+xy dx у2+1

A: we have the differential equation dydx=2x++xyy2+1 or (2x+xy)dx-(y2+1)dy=0 we have to find the…

Q: B) Solve the equation (x+y-1)³ dx+4(x-2) dy=0.

A: Solution

Q: Quiz Solve a Bernoulli's equation. dx 2X dy vg (x

A: The detailed solution is as follows below:

Q: dy Find the general solution of 2x² = a? + y? dx %3D

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Q: identify the substitution equations and solve the solution 2( x–y)dx+dy=0

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Q: Find the general solution of the equation, d²y dy 4 + Зу %3D0 dx dx?

A: Since you have posted a multiple question according to guildlines I will solve first question for…

Q: Q1. Solve the following first order equations: (a) (r²y² + 1)dx + 2x²dy = 0, use the substitution ry…

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Q: Solve and find the domain in which the solution is defined. dy/dx = (y2-xy-x2)/x2 , y(-3)=-6

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Q: 9= (X-1) Cx-2X) %3D

A: To solvey=(x-1)(x2-2x)x4.

Q: v3 du + (u uv²) dv = 0. Solve the given equation

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Q: Show all solutions. Find dy and evaluate when x=2 and dx=0.2. y=xe1-2x

A: For an equation of the form y=f(x) the differential is calculated by differentiating with respect to…

Q: Solve the equation: dy 2y -a²y? sec² (x) dx

A: Given dydx+2yx=-x2y2sec2(x)

Q: Determine whether the equation is exact. If it is, then solve it. (3x'y +2 ) dx+ (x-3) dy D0

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Q: Solve the equation with Lagrange to find general and particular solution y = (2+ y')x + y²

A: The given differential equation is y=2+y'x+y'2            ......(1) This equation is of the form y=x…

Q: Solve the attached equation by variation of parameters ?

A: d2ydt2+y=sec xy''+y=0m2+1=0m=±i α+βi, α=0, β=1 Yc=c1eαxcos(βx)+c2eαxsin(βx)Yc=c1cosx+c2sinx Y1=cos…

Q: Test the equation for exactness and solve the equation: (1+ y?)dx + (x²y + y)dy = 0

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Q: Q4. The degree of the equation is dy d²y dx dx?

A: degree it is the degree of higher order derivative term here higher order derivative is d2y/dx2…

Q: Solve the diff eq (ху?+x-2у+3)dx +(x?у — 2х - 2у)dy %3D0

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Q: Find all values of the constant c so that (2x + y) dx dy = 3.

A: Given: ∫01∫0c2x+ydxdy=3 To find value of c. Solving the given integral, we get…

Q: (2xy²-2y) dx +(3x²y - 4x)dy = 0

A: The given differential equation is;  (2xy2-2y) dx+(3x2y-4x) dy=0

Q: Solve the equations and simplify the final answer. 1. (x + y- 1) dx + (2x + 2y +1) dy = 0

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Q: Bernoulli's Equation dy = y – xy³e-2x (final answer should be in terms of y) dx

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Q: dy x + 2 dx (dy / dx)

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Q: Solve the differeial equation: dy/dx=3x^2y^2

A: The given differential equation is dydx=3x2y2.

Q: (2у^2 х - у) dx +xdy %3D0

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Q: Solve the equation with Lagrange to find general and particular solution y = (2 + y')x + y'2

A: Given: Equation y=2+y'x+y'2 To find: General and particular solution using Lagrange's method

Q: dy .? dx %3D Suppose x and y are variables that satisfy the equation x2 – y³ = 12. What is

A: We can find dy/dx as below.

Q: Q6// Solve the equation: y cos? x dy + sinx dx = 0.

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Q: Solve the equation using Variation of Parameter:  (D^2 + 1)y = sec^(2x)csc x

A: Given that: (D2+1)y=sec2x.cscx

Q: dy/dx=(x+3y-5)/(x-y-1) solve this diff.equation

A: Consider the given differential equation. dydx=x+3y-5x-y-1 Put the following values in the equation.…

Q: Exact equations (бх + у?)dx + yу(2ху — Зу?)dy %3D 0

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Q: Solve the equations and simplify the final answer. 1. (2x– 3y + 4) dx + 3(x– 1) dy = 0; when x = 3,…

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Q: SOLVE THE DIFF EQ (ху-бх?)dy - (2y2-9ху)dx

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Q: . Given dy/dx = −2x + 6, find the equation of the curve that passes through the point (2, −2)

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Q: а) (у — х)dy + y dx %3D0 dy у-х+1 b) dx у-х-6

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Q: Solve the equation (show all step) (Xsiny)dx+(x²+1)cosydy3D0

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Q: Find only the particular solution of the following equations (a) +y =cos 2x dx" (b) -52+6 y =7 dx dx

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Q: Given (x² + 2y)dx + (+ 2xy+ 2x) dy = 0. 3 i) Check the exactness of the equation. ii) Based on your…

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Equations and Inequations

Equations and inequalities describe the relationship between two mathematical expressions.

Linear Functions

A linear function can just be a constant, or it can be the constant multiplied with the variable like x or y. If the variables are of the form, x2, x1/2 or y2 it is not linear. The exponent over the variables should always be 1.