Solving the question by nonhomogeneous equation Not: without using themethod of variation of parameter d²y +y = tan x %3D dx2

Q: Vx/3+1 dx x2/3

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Q: follerving initial value problems by separating the Vasiables Solve the ye)=2 %3D %3D dx

A: Solution:Givendydx=y2-1x2-1; y(2)=2Formula:log ab =log a +log blog ab =b log aa2-b2=(a+b)(a-b)∫1x…

Q: (xy² + y-x) dx + x(xy+1) dy = 0

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Q: (x – y – 2)dx + (3x + y – 10)dx = 0 -

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Q: Determine the form of a particular solution yp of Ур y" + 4y = x cosx. Do not solve the equation.

A: Here given the differential equation as y''+4y=xcosx or D2+4y=xcosx where D=ddx

Q: Q.5: Solve (1+ y²) dx + x dy – tan-1 y dy = 0.

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Q: 2. +y = (1 + 3x)r

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Q: Using the method of variation of parameters solve the following. d2y/dx2+ y = tan x.

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Q: Consider the equation, test whether it is exact and solve the IVP.        x(x-y)dy = y(y-3x)dx…

A: solGivenx(x-y)dy=y(y-3x)dx

Q: Consider the following. dy - - X dx %3D

A: given equation is, dydx=-xy

Q: The Method of Variation of Parameters (4) Find the general solution of y" + y = tan x, 0 < x < Tt/2.

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Q: Using the method of Variation of Parameters, the particular solution y, for the NHLDE y"+y=sec x js

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Q: 4. General solution of (y2 + xy) dx – x² dy = 0 %3D

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Q: P/ by method of variation of Parameters -X find ゾーン Y-Y = e Sine

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Q: У (4х + у) dx — — у) dy 2 (x² - 2x2 +x+ 2In у — С ans. y

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Q: . Given dx y + x (a) Solve the equation (b) Verify that your solution in part (a) is an implicit…

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Q: Variable Separable D.E. O 2. Solve the equation: 3x²(1 + y²)³/2 dx – dy = 0.

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Q: Use l = PRT to solve. %3D (time is in years) | = $300 P = $3,000 T= 0.5 years Find R. [?]% %3D

A: Given data,I=$300P=$3000T=0.5 yearsFind R?

Q: • Find solutions using Exact Equation (show step by Step soLution good hand written) 1.) Sove ex…

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

A: The detailed solution is as follows below:

Q: Test For Exactness, if Exact, solve. 1. (3x2y+2e2y+3)dx + (x3+4xe2y-sech2y+2lny-y)dy=0

A: The equation is exact as My=Nx, and the solution follows as:

Q: Solve this completely to answer several questions. dy 4y Consider the equation + = x. dx What is the…

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Q: 1. [D³ – 6D² + 11 D - 6) y = cos x sin x

A: To find solution of differential equation

Q: y" – 2y' + y = 1+a? 2

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Q: dx Simnlify - [d2+x²]?

A: The given integral is ∫-∞∞dxd2+x232 first calculate the integral ∫dxd2+x232 substitute x=dtanu…

Q: Linear Equation x? dy – sin3x dx + 2xy dx = (final answer should be in terms of 0)

A: We have to solve

Q: Using Homogeneous Equations, find the general solution of the equation below. dy dx x-y y

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Q: Differantial equations 4 questions   (dy/dx)+(y/x)=(x/y^3)

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Q: Solving by variation of parameter y" – 2y' + y = e* log x, the value of W(y1y2) is

A: Let's find.

Q: Hw3] Find )xsin(x?) dx

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Q: (4x® y-18x² + y)dx+(x* + 3y +x)dy= 0

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Q: Question: Solve for y'(6) Equation: F(x)=( X² + 1 )/ X Show your solution (Use Long Method only,…

A: We have to find the derivative of the function F(x)=x2+1x at x = 6.

Q: 3. Determine the general solution to the equation xy' = (1+ x) sec(y), x > 0. You can leave your…

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Q: 1. Do you need using substitution method to solve (x2 – 9)(2x)dx ? If yes, please identify u and…

A: Since you have asked multiple questions in single request,  So we will be answering only first…

Q: Solve using Bernoulli's Equation y'+xy=xy-1

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Q: P/ by method of variation of Parameters -X Find Y-Y = e sine دیگا

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Q: Exact equations: Solve * (2x + 3y) dx + (3x + y - 1) dy = 0 O x* + 6xy + y² – 2y = c O y2 + y* = c

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Q: dx2 doc sin@ags) Ans: y =x² (A z3 + (5sin Clox) + G coslog.s>) +Bx 61て

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Q: Using Integrating Factor by Inspection, solve: (y − xy²) dx + (x + x²y²) dy = 0

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Q: 1. Bernoulli's Equations: Solve the equation y (6y? – x – 1) dx + 2xdy = 0

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Q: 2y(x2 – y + x)dx + (x² – 2y)dy = 0

A: Consider  Mdx+Ndy=0If ∂M∂y=∂N∂xThe the equation is exactIf not exact, we find the integrating…

Q: 3-x If j- dx = x(x – 1)(x +2) +. x+2 When A, B, and C are solved, what is the value of their sum or…

A: Given ∫3−xxx−1x+2dx=∫Ax+Bx−1+Cx+2dx.....1 We have to find the value of A+B+C. Take partial fraction…

Q: The Method of Variation of Parameters (3) y" + 4y = sec x

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Q: Solve this completely to answer several questions. Consider the equation + Y x. dx What is the…

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Q: If variation of parameters method is used when solving the equation y" 1 then what is the vz (x) of…

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Q: Find the general solution of the equation. Express the solution explicitly as a function of the…

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Q: Solve using variation of parameters: y" - 2y + y = e¹/(1+1²) + 3et p= ₁ ² + ₂ tet (Use 2 decimal…

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Q: PART - B IA. Solve (4xy + 3y? - x)dx + x(x +2y)dy = 0 with y(2)=2. IB. Solve (x²D2 + xD - 1)y =ri

A: Since, you have posted multiple questions. As per guidelines we will solve only first question. If…

Q: Using Substitution Techniques solve for the implicit solution dy/dx = tan(x+y)

A: Given that dydx=tan(x+y) Take U=x+y And, Y=U-X Then, dydx=dudx-1