FIND THE PARTICULAR SOLUTION: SHOW SOLUTION AND PROVE THAT THE EQUATION (y4-2xy)dx+3x2dy=0; when x=2, y=1 HAS THE ANSWER OF x2=y3(x+2)

Q: Solve the following using exact equation or linear whichever is applicable. (2xy − 3x²) dx + (x² +…

A: We are given: (2xy − 3x²) dx + (x² + y) dy = 0⇒M=2xy − 3x²⇒N=x² + y ∂M∂y=2xand ∂N∂x=2x Hence, this…

Q: Solve the given Ricatti equation dy = e2* +(1+2e* ]y +y²,y, =-e*is a known solution of the equation.…

A: Given, the Ricatti equation                                                 dydx=e2x+1+2exy+y2…

Q: SHOW THE SOLUTION OF: 25 - 2xy dy CHOICES: A.) y = x'(x+c) B.) y = x(x+c)? C.) y = x(x+c) D.) y =…

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Q: Solve the following using exact equation or linear whichever is applicable. (x + y) dx + (x − y) dy…

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Q: Solve the given DE using 3 possible solutions: y' X 3 - 2y 3 3xy 2

A: Given DE  y'=x3-2y33xy2  …………………………(i) we can write it as dydx=x3-2y33xy2

Q: (x² + 4xy + 2y²)dy + xydx = 0

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Q: d²y - y = у 3 10sin?x %3| dx2

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Q: Determine for which values of m the function 4(x) = x" is a solution to the given equation. Ta) 2x…

A: Hey, since there are two questions posted, we will answer the first question. If you want any…

Q: 9. (x +y) dx – (y – x) dy = 0; y (1) =1 %3D

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Q: A. Find the general solution of y" = 12x². dy B. Solve for y F dx - 4 x²-1

A: The given differential equations A) y''=12x2 B) dydx=4x2-1 use the integration formulas,…

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

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Q: x4+a* dx x3 5. S ydy Va?-y2

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

Q: Use any appropriate method to find the general solution of each of the following equations. dy - y²…

A: Given differential equation is, x2dydx-y2=yx+x2

Q: Solve: (4x3y−18x2−y)dx + (x4+3y2−x)dy = 0 a) Check for exactness b) If the equation is exact,…

A: Exact differential equation

Q: Show that the DE is exact, then solve it. (2.x +1- y/a²) da + (2y/x)dy = 0, y(1) = 1

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Q: Use appropriate substitution to reduce the following equation to a variable separable and then dy 3x…

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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: Given that d²y 2. +y =0. dx2 Show that y = x is not Solution a

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Q: Given the equation: dx + xydy = y^2dx + ydy. Solve for the solution when x = 3 and y = 0 1. _____…

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Q: 5. (D² + 4D + 4)y = 0 ;when x = 0,y = 1,y' = -1

A: Given equation is, D2+4D+4y=0, x=0, y=1, y'=-1 Now, write the auxiliary equation for the given…

Q: B. In each exercise, obtain the particular of solution. 2. y(9x - 2y) dx - x(6x – y) dy = 0; when x…

A: Differential equations

Q: Obtain the general solution unless otherwise instructed d²y 1. dx2 - y = 10sin²x

A: You have asked multiple questions and not mentioned which question answer you need so according to…

Q: Obtain the general solution to the equation. dx + 4x = 2y7 dy The general solution is x(y)=,…

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Q: SOLVE NHLDECC USING VARIATION OF PARAMETERS. 1 (D2 + 2D + 1) y = (e*-1)² ANSWER: y = e¯x (C1 + C2x -…

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Q: e-SP(x) dx Y2 = Y(x) (5) as instructed, to find a second solution y,(x). y" + 2y' + y = 0; y, = xe*…

A: We will find out the required value.

Q: d³ y dx³ 2d²y dx² 1 3dy=0 dx

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Q: Solve for the solution for the equation: (x² + 3xy)dx + (x² + 4y) dy = 0 with the condition of y(2)…

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Q: Find the complete solution of (x?y +y³ – y)dx + (x³ + xy² + x)dy = 0 Hint: Expand and Simplify

A: Hey, since there are multiple question posted, we will answer the first question. If you want any…

Q: Obtain the general solution unless otherwise instructed 3. (D² – 3D + 2)y = e2*(1+ e2x)¯1 SUMMARY OF…

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Q: d³y d?y dy dx3 dx3 - y = 4 sin x dx

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Q: Find the solution to the Bernoulli Equation. 2x³y = y(y? +3x?)

A: The solution is given as

Q: c) Show that y(x) = 1+ax+bx², where a and b are non-zero, is a solution to Laguerre's equation, d²y…

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Q: (D² – 3D + 2)y = e2*(1+e2x)

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Q: Obtain the general solution using Bernoulli's equation. Simplify your final ansv answer. ix- 6* dy =…

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Q: Obtain the general solution unless otherwise instructed . (D² − 3D + 2)y = e²x(1 + e²x) −¹ Yc = Ур =…

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Q: #3 Test the exactness and solve the equation. (2xy 3x²)dx + (x² + y)dy = 0

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Q: solve the equations by using Bernoulli's equation. 1) x^2.y' - y^3 = xy 2) y' + p(x)y = f(x)y ln y

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Q: Solve the equation with homogeneous coefficients. (3y² – x²)dx – 2xydy = 0

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Q: (c) Test for exactness and solve the IVP, critically outline the particular solution (x + 5e*y)dx =…

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Q: Q1) solve all these first order diff questions with appropriate method of solutions dy _ y²+xy?…

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

Q: 5. (1+ y² + xy²)dx + (x²y+ y + 2xy)dy = 0

A: The differential equation is given as 1+y2+xy2dx+x2y+y+2xydy=0 Compare it with Mdx+Ndy=0 Here M =…

Q: Given (x + 6y? ) dx - 4xdy = 0, when x = 1, y = 1. Find the particular solution.

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Q: Prove that the equation below is a homogenous one and solve for its equation. 3(3x2 + y?) dx – 2xy…

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Q: y dx + (3x – xy + 2) dy = 0 -

A: As per the instruction, we will be solving only the first one. For (4),We will solve it by Exact…

Q: • Use the mothed of variation of parameters to find the general solution of the following equations.…

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Q: solve fos given, dy 2. -2t "ट +-

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Q: Solve the equation. (+5x) dx+ e*y dy = 0 An implicit solution in the form F(x,.y)% C is =C, where C…

A: To solve: The equation x3+5x3y4dx + ex4y3 dy = 0 .

Q: Use the mothed of arlation of parameters to find the general solution of the following equations. a)…

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Q: Determine the constant A such that the equation (x2 + 3xy) dx + (Ax² + 4y) dy = 0 is exact and solve…

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Q: (2xy - x + 2y - 1) dx + (4x²y² - x² + 4xy² - x) dy = 0

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