7. Find the general solution: y(x? + y²)dx + x(3x² – 5y²)dy = 0 a. y³(y² – x²) = cx b. 2y3(у2 — х?) %3 сх с. Зу? (у? — х?) %3 сх d. 4y3(y2 – x²) = cx -

Q: 4. Find the particular solution of y(x² + y²)dx + x(3x² – 5y²)dy ;where x = 2 and y = 1. -

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Q: Find the general solution of x(x + 3)dy = 2dy + √(9- y²)(12x + 9 + 4x²) dx.

A: We will separate variables and then will integrate it to find general solution of given differential…

Q: Find the general solution of the DE (2y – x2) dx + (y+2x) dx=0 А) 2ху + 3 y2 =C 2 (в) 2ху — 3 x3 y2…

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Q: Use the method of variation of parameters to find a particular solution of y" – 5y' + 4y = e*. %3!

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Q: 10.Obtain the general solution of y(8x – 9y)dx + 2x(x – 3y)dy = 0

A: First we find tha integrating factor of given differential eq then we get exact differential eq.So,…

Q: fud General Solution dy-3y=

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Q: ) Obtain the general solution of y" + 2y + y = e² In r

A: In this question, the concept of the differential equation is applied. Differential Equation A…

Q: Determine the General Solution of ye2x dx = ( 4+e2x %3D ) dy

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Q: The integrating factor of the equation (xlnx)y' + y = 2lnx is || Select one: a. ex O b. Inx c.…

A:

Q: Find the general solution of using the method of variation of parameters. d²y dy 2- - 42+ 2y = xe 2x…

A: Given,2y"-4y'+2y=xe2xComplementary SolutionAuxiliary Equation is 2m2-4m+2=0⇒m2-2m+1=0⇒m-12=0⇒m= 1 ,…

Q: fin the general solution of (x+2y-4)dx - (2x+5-y)dy=0

A: Please see the below picture for detailed solution.

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A: Given differential equation is y'=y(x+y), step size h=0.1 with initial condition y(0)=1 Let x0=0,…

Q: В. NON-HOMOGENEOUS HIGHER ORDERED LDE 1. (D3 + 5D² + 3D - 9)y = 64x²e-3x 2. (D³ + 13D - 34)y = 25x2…

A: As per our guidelines, we are supposed to solve only first question. Kindly repost other question as…

Q: 3. Show that the equation (6ry – y*)dx + (4y + 3x² – 3xy²)dy = 0 is exact. Hence solve the equation…

A: Solution:

Q: use Separation of Variables to find the general solution. yy' = x

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Q: dy Solve of y = e2-3+18 In(e2²-30+18 da A. y' e2z²-32+18 (8x3 – 18z² + 85x – 57) B. y' e2a2-3a+18…

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Q: Find the particular solution of -4y = 3x – 1 given that when x=0, y=0 and d2x dx dx II

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Q: Solve (D2 – 2)y =0 O a. y = cqevZx + c2e¬vZx O b.y= "(c,cos/2x+ c,sin/2x) O c.y = cqevZx+czxe¬VZx O…

A: The equation D2-2y=0 represent y''-2y=0 . Consider the solution of the differential equation is in…

Q: Find general solution of y" – 2y' + y = , By Variation of t2+1' parameter method.

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Q: 6. Find a general solution to the third order equation y" + y" + 3y – 5y = 0.

A:

Q: A Q2 Show that y=x+ is the solution of 3x – x = x+ y. dy dx

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Q: value of c in the equation: dV/dt = -500 (t+1)-2, when  V=700and t=0 is

A: follow next step

Q: Obtain the genral solution. (D³ +5D²+7D+3)y=0 y=eX(C₁-C₂x) + С3e-³x + С₂e-³x Oy=eX(C₁+C₂x)…

A:

Q: y" + y" = 3

A: Solving the given third order differential equation

Q: 2. (D² - 3D + 2)y=1+x

A: The given differential equation is;  (D2-3D+2)y=1/(1+e-x).

Q: What is the general solution of xy(xy5 −1)dx + x²(1 + xy5) dy=0 ? A 2x³y³-3x²= Cx² B 2x³y5-3x²=Cy²…

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Q: solve the Initial Value Problem using Separation of Variables. y' = xy2, y(1) = 2

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Q: Given the initial condition y(1) = 4, what is the particular solution of the equation = Y Vx²+3 :?…

A: Option C is corect...

Q: 4. Find the solution of (x²+6y²)dx – 4xydy=0 when x=1, y=1. Use Substitution Method.

A:

Q: What is the general solution of the given DE m2y = C,e™1* where C1, m1, m2 are constants dx and m, +…

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Q: 3 Solve dx₁ de dx2 dt = the 2x1 1 following 5x2 -cost x12x2 + sint system. a) by using the method…

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Q: Solve for the general solution * (4xy+3y – x) dx + x (x + 2y) dy = 0 x' (4xy² + 4y – x) = c x²…

A:

Q: 8. Find the particular solution that satisfies the initial condition. y'+y = 6e*, Initial Condition:…

A: Find the particular solution

Q: 2) .. Use separation of variables to find the general solution.   dy dt − 12t3e−y = 0.

A: Answer: The solution is as given below:

Q: What is the solution of (xy? – x) dx + (a²y + y) dy = 0 when x = 0 and y = 3 %3D O (22 - 1) (y² – 1)…

A: Exact differential equations.

Q: What is the solution of (2x - y)dx + (4x + y– 6) dy = 0? а. (x+у-3)°- с (2х +у- 4)? b. (x-y+3)²=…

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Q: dy - Find the general solution of Y +2 = 3x²y² dx A. 1/(xy) = -3(x³/2) + C B. 1/(xy) = -3(x²/2) + C…

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Q: Solve the DE using Linear First Oder Method: y +yx = x - 3. if y(0) = 2 %3D

A: Given y'+yx=x-3   if y0=2 To find the general solution

Q: 2. Find the particular solution of Vx2 + y2 )dx – x dy = 0 ; y = 1 when x V3. -

A: Given differential equations homogeneous differential equation of first order we will do the…

Q: solve the problem by method of characteristics  y du/dx -4xdu/dy = zero  where the initial…

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Q: What is the general solution of differantial equation?  Whicf of the options x² - y² + xy dy/dx =0

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Q: Find the particular solution for (2y³ – x³) dx + 3xy² dy = 0 when x = 1, y = 1 A. 5x²y³ = x³ + 4 B.…

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Q: (Think homogeneous) Solve explicitly (y² - xy) dx + x²2dy = 0

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Q: What is the general solution of xy(xy³ −1)dx + x²(1+xy5)dy=0? (A) 2x5y³-3x²= Cx² B 2x³y5-3x2= Cy²…

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Q: Find general Solution of y + +y+ 4y = Ct1)e Using method of vanafion.

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Q: Show that xy – 2 = cxy is a solution of (x² + y2 – x)dx – ydy = 0.

A: Given  x2+y2-xdx-ydy=0 dydx=x2+y2-xy

Q: 4. Verify that y=cx+e² +1 is a solution of the equation y=y'x+(y')' +1.

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Q: Solve for the general solution. d³x dx -7. - + 6x = 0 dt3 dt

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Q: Obtain a particular solution for + + +y = x³ + 2x + 1 dºy, d²y dx4 dx²

A: