y = Cje² + C2xe* + C3x²e* %D O y" + 3y" + 3y' + y = 0 y" – 3y" + 3y' + y = 0 %3D + 3y" + 3y' – y = 0 %3D - y" - 3y" + 3y' – y = 0

Q: The standard form of 3dy – xydx = 3y³e¹x/³ by Bernoulli's equation is: dx A d 2=3e dy ху B D…

A: Solution : Given that

Q: 9. dy/dt = y²(y² - 1), -∞ < Yo <∞

A:

Q: The particular solution of y(x+y)dx + (x +2y- 1)dy=0; y(0) = 2 by NEDE is

A:

Q: Solve system of linear DEs  dx/dt+dy/dt+2y+6y=2e^t 2dx/dt+3dy/dt+3x+8y=-1

A: To solve dxdt+dydt+2x+6y=2et2dxdt+3dydt+3x+8y=-1

Q: dx/dt+dy/dt+x=e-t dx/dt+dy/dt-x-y=e2t x(t) general solution function

A: Given equations are                                              dxdt+dydt+x=e-t           ...…

Q: Find the solution. Zy dx = (-1dx - dy) A (x-1)x = (y+1Xc - 2x - In|y-1|) B (x-1)y = (x+1Xc +x -…

A: First re-arrange the given differential equation. 2y dx=x2-1dx-dy2yx2-1=dx-dydxdydx+2yx2-1=1

Q: + 4 2+ 4 y = 0 with y(0) = 1.5 and d²y dy dy (0) = 0 dt² dt dt

A: Given initial valve problem is: d2ydt2+4dydt+4y=0  ⋯⋯1 with  initial conditions y0=1.5 and dydt0=0…

Q: 2. Identify the 3rd order nonlinear DE. 3 A. O +xy – xy³ = 0 8.+ y=0 d³y В. d²y d³y dx³ d²y +x- dx…

A: Given query is to find the third order non linear differential equation.

Q: d²z 2+ 3-2z = te-2t ; z(0) = 0 z'(0) = -2 dt2

A:

Q: (xy² + 3y²)dy – 2x dx = 0 is not separable. ylgn ihi

A:

Q: 2y dr - y dy y (x-2y) dy, y(0) =-1 O x = 2y - e +3 %3D a y = 2r- e+3 0x= 2y-e+3 O x = 3y + 2e +1

A: Given DE is 2y dx-y dy=y(x-2y)dy ⇒dx-12dy=12(x-2y)dy⇒dx=121+x-2ydy⇒dxdy=12+x2-y⇒dxdy+x-12=12-y Which…

Q: Find the equilibrium solutions for dy = -2 + 3y – yʻ dt .2

A:

Q: Solve (x – y)dx + (3x + y)dy = 0 with the condition: y(2) = –1 O (2æ + 4y) – (2x + 4y) ln(2x + 4y) =…

A:

Q: ý =y+X ans y= as +aoX+(a+). %3D a. %3D e +e-X-1

A:

Q: dx 3 3х-Зу+4 dt dy %3D 2х-2у-1 dt O A. x = 3c1e + c2- 15, y = 2ce + c2-10 – 11t O B. x = 3C1e + c2-…

A:

Q: 3. 2y dr - (2x + y) dy = 0 x = y In cy y = x in cy %3D = x In cx 2x = y In cy %3D %3D

A: The solution of the problem is given in the next steps.

Q: The DE dy/dt = µy – oy², µ > 0 and o > 0 occurs in the study of population dynamics. It has general…

A:

Q: A _1. (2x – 3) dx A. -2 _2. L(x3 + 2x) dx В. 0 _3. (x² – 2) dx 1 С. 3 4. S(x3 + 3x – 1) dx 2 D. 2 |…

A:

Q: 6. Find the (xy + 1) dx + x (x + 4y − 2) dy = 0 integrating factor and solve DE. In x + xy + 2y (y −…

A: A detailed solution is given below.

Q: d³y dt3 dy + 4 dt2 + 5 dt + 2y = 10 cost y(0) = 0, y'(0) = 0, y"(0) = 0 %3D

A:

Q: Obtain a family of solution a. (x -y ln y + y ln x)dx + x(ln y - ln x)dy = 0

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Q: (2t - 4 0st<2 (D2 – 1)y =- 12 %3D t22 y(0)=0, y'(O)=1 Find L{y} L (y) = F1) 4 2e-2s 2e-2s %3D -…

A:

Q: 1. y" - 2y' - 3y = e* by D- operator method

A: Since you have posted multiple questions so according to our guidelines we will solve only first…

Q: 6. Find the general solution to the system of equations dx dy + dt dt 2t + +x+y=0 d²x dx dt² dt

A:

Q: (3y' + y)/y = x (1) y' - 3x'e-Y = 0 (2) y In y dx + (x + y)dy = 0 (3) xy' + y = sin x + 2 cos x (4)…

A:

Q: e. dt2 d²y dy + 4y = 8t – 10, y(0) = 1, y'(0) = 7 dt f. 3- dy 3– 2 - y = 2y – 1, y(0) = 7,y'(0) = 2…

A: Since you have posted multiple question and according to guidelines we will solve only one question.…

Q: 1.)(x + y - 1) * d * x - (x + 4y + 2) dy = 0

A:

Q: 6. Find the general solution of (cos cos y +ycos x) dx+ (sin sin x – x sin sin y ) dy = 0 A. x cos y…

A: As per the guidelines I am supposed to do the first question among multiple questions. So I am…

Q: ə)o y"-2x°y"+y'= 0 xy - xy'-y' In(x) C) O ge 3y"+y' e* cos x d) y y+ xy"-y 0 3. e) y"-2 y) +y 0

A: We will use elimination technique to answer this question by eliminating options which do not…

Q: 3. Find the general solution of the system: dx = r+ y dx dy — 2л — у dt

A:

Q: 2 (xy + x) dx = (x²y² + x² + y² + 1) dy Oln(x² + 1) = y² – 2y — 4ln|c(y + 1)| O In (x² + 1) = y² +…

A: We have to solve given differential equation. The given differential equation is…

Q: Find L(y). / + 2x = 2 - x' = et (0) = x (0) = 0 -2 L (y) PL(y) = %3D s(s2 +2) 2s L (y) = %3D…

A:

Q: Solve [y (In x – In y) + x] dx +a (In y – In a) dy = 0 xlny + yln x = Cx None of the choices ylnx +…

A:

Q: Find the general solution of the given system. dx/dt = -(5/2)x + 4y dy/dt = (3/4)x - 3y =________

A:

Q: (2) An integrating factor of (xy³ + y)dx + 2(x²y² + x +y*)dy = 0 is (a) y (b () (d) 2xy

A: We need to find an integrating factor of xy3+ydx+2x2y2+x+y4dy=0 Now, a differential equation of the…

Q: 1. 2y" + 3y – 2y = te-2t ; y(0) = 0, y'(0) = %3D 2. dt *+ y = e2t ; y(0) = 0

A: A detailed solution is given below.

Q: 2. Identify the 3rd order nonlinear DE. 3 +x³y – xy³ = 0 \dx) d³y d²y +y dx? В. = 0 dx3 d³y d²y С.…

A:

Q: 2t-4 0st<2 (D2 - 1)y = t22 y(0)=0, y'(0)=1 Find L{y} L (1) = 1 + - - 2+ 4 2e 2s 2e-2s %3D | L (y) =…

A:

Q: 5. y' + 2y = 0, when x = 0, y = 2 %3D Ans. y = 2 e-2x %3D dy 6. xy +2 y– x - 2 ху — Зу+х-3 dx (у -…

A:

Q: dx dt dy dt = 1 6 (x−1)(5−x− 6y x ) = y 20(1− y x−1) Find the nullclines  of the system

A:

Q: Consider the system dx dy 1+3y, dt -1– 5x? dt a) Find all the critical points (equilibrium…

A: Critical points

Q: () fiz) - y-2xyy ti(-x+ x² y+) + z* そ=メー *y メ eうあ* *y* (-anaty'n g) u cory) +i vexy) 三 wy) = *y*x ;…

A:

Q: 1. Determine the general solution of (x 3y )dx – x dy = U

A:

Q: (i) (iv) (vii) dx x2 dx = (x + 1)(y² – 1) dx 1 –x² + 2x – 1 %3D = - | dt dt dt dy dy dy = x² – 2x +…

A:

Q: 3. Find the general solution of the system: dx = x + y dt dy -2x – Y dt

A: Given dxdt=x+y and dydt=-2x-y

Q: 3 * (dx)/(dt) + (dy)/(dt) + 2x = 1, (dx)/(dt) + 4 * (dy)/(dt) + 3y = 0  Given x = 3 y = 0 when t =…

A: As per the question we are given the following system of differential equations : 3x'(t) + y'(t) +…

Q: Solve (xy + x)dx = (x² y² + x² + y² + 1)dy. O In(x² + 1) =y² - y + 2 In (y + 1) + c O 1/2 In(x² + 1)…

A:

Q: The particular solution of y(x+ y)dx + (x+ 2y- 1)dy=0; y(0)= 2 by NEDE is

A: Let's find.

Q: 2- y(x + y +1 ) dx – x(x + 3y + 2)dy = 0 Reducible to Exact Method

A: We have to find general solution of given differential equation which we reducible to exact method :…

Q: Reducible to dy 2х-у+4 homogenous method dx x+y-1

A: