Arrange the terms of the equation in a linear form and evaluate the quantities P and Q using the formula y = e-SP(x)dx[S Q(x)eS P(x)dx dx + C] if the equation is linear in y, and x = e-S P(Y)dy[S Q(v)eS P(y)dy dy + C] if it is linear in x. %3D 1+sinx 1) y' +y = Ans: y = tan+ ce¬* 1+cos x

Q: The general solution of the D.E.  ( x + y)dx + (x-y)dy = 0.

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Q: Find the general solution of the equation x(y2 + 1)dx + (1+ x²)dy = 0. A. In(x2 + 1) + 2Arctan y = c…

A: The given equation is; x(y2+1)dx + (1+x2)dy =0

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Q: Find the general solution of the given D.E. 2x(3x + y – ye-*´)dx + (x² + 3y² +e-x*)dy = 0. %3D

A: Shown below

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Q: (H.W) 1- Solve by choose M this time (2 x y² + 3 x² ) dx + (2 x² y + 4 y³ ) dy = 0 2- Find the…

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Q: Find the particular solution of the given ODE. ( y − √x² + y²) dx − xdy = 0 when r = √3, y = 1 - -

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Q: B) Find the general solution of the equation by using (Undetermined Coefficients method) d'y dy de =…

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Q: You are given a first-order D.E. = x2 + y³ . Suppose the solution y(x) satisfies the initial dx…

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Q: Given the initial condition y(0) = 1, find the particular solution of the equation

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Q: Given the Bernoulli's equation Dy/DX+yP(x)=y^n Q(x) and x=y^1-n, reduce the equation to the linear…

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Q: Find the complete solution of the following D.E. d³y dy? dx2 dy - 85y = x2 + 16 e* 4- + 12 | dx3 dx

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Q: (xy)dx + e*dy = 0, as xo, y =D;

A: Given:- (xy2) dx + ex dy=0 To find:- Particular solution of given differential equation

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Q: Find the solution of the D.E. xydx - (x? + 3y) dy = 0 Show your solutions on a separate sheet of…

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Q: dy 1. 6x², y(0)=5 || dx dy 2. dx e* +4 e* y(0)= In 5 '

A: “Since you have posted a question with multiple sub-parts, we will solve first three sub-parts for…

Q: The point of intersection when the coefficients of dx & dy are equated to zero of the given DE:…

A: Here I am attaching image so that you understand each and every step.

Q: From the following equations select the one that is not exact and solve. (x2- у) dx — х dy%3D0 1.…

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Q: 3x3 d'y If y = + find dy and dx (a) 3 2 dx2 (b) If f(0) = 4 cos 30, find f'(0) and f"(0) and…

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Q: Is the equation separable, linear, bernoulli, or homogenous? dy а. dx x4 + 4xy² 2x3 + x²y +y³ b.…

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Q: dy e y- e-Y +e-2x-y 1. dx

A: Since you have posted multiple questions in this question which are not interlinked so I have solved…

Q: Except for degenerate cases, the equation Ax2 + Bxy + Cy2 + Dx + Ey + F = 0 defines a(n) _______ if…

A: Given: Except for degenerate cases, the equation Ax2 + Bxy + Cy2 + Dx + Ey + F = 0 defines a(n)…

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Q: III. Find the particular solution of each of the following. dx 1. dy 2x - 7y*; when y=1,x=-1

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Q: r1 -x²-y² •1 p? sin ф dp dф d@ 1+ p2 dz dy dx is equivalent to 1+ x2 + y? + z2

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Q: solve the differential equation with the given initial condition.

A: We separate the variables and then integrate both sides. C=integrating constant

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Q: Find the General Solution (D² – 3D + 2)y = cos(e¬*)

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Q: Solve the following equations: a) y√(1-x²)dy + x√(1-y²)dx=0 x(2 ln x+2) dy = b) dx sin y+y cos y…

A: note : As per our company guidelines we are supposed to answer ?️only first 3 sub-parts. Kindly…

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Q: find the general solution of the given equation. d2y/dx2 + 4 dy/dx + 4y = 0

A: d2ydx2+4dydx+4y=0 The auxiliary equation is, r2+4r+4=0⇒r+22=0⇒r=-2

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

Q: Solve the Bernoulli equation dy + xy = xy dx y = (ce²² – 1)-} .B y = (ce² +1)-} .C y = (ce²² + 1)-}…

A: Thanks for the question :)And your upvote will be really appreciable ;)

Q: Is the equation separable, linear, bernoulli, or homogenous? dy а. dx x4 + 4xy2 2.13 + x²y +y³ b.…

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Q: 3. Find an explicit family of solutions for the following equation: x² dx 3у — ху. dy 3y = x with…

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Q: Solve the DE: 2(x+y) dx- x(x+2y-2) dy=0 A 2xy+ x2 = Ce* B 2xy-x²= Cey 2 ху - х2 - Се* none of the…

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Q: Find the general solution of D.E. below: (x-2y) dx + (2x+y) dy = 0

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Q: Find the constant a so that e"y + y = x – 1 is an implicit solution to -TY +ay dy dx e e-ry+x O -5/2…

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Q: (H.W) 1- Solve by choose M this time ( 2 x y² + 3 x² ) dx + ( 2 x² y + 4 y³ ) dy = 0 2- Find the…

A: If the differential equation Mdx +Ndy =0  is exact ∂M∂y=∂N∂x , then solution is                 ∫y…