Find solutions using Exact Equations 2. Solve (3x*y? – x²)dy + (4x³y3 – 2xy)dx = 0

Q: Find the solution of the homogenous equation: 2(2x2+y2)dx-xydy=0

A: The given differential equation is  2(2x2+y2)dx -xy dy=0

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: . Find the general solution of the first-order equation y? – 2ry dy dr

A:

Q: (x +2y-4) dx + (ax-4y ) ay Solve by Coerlaents linear in two variable

A:

Q: dy = -8xy² dx 3. Solve + 4x(4x+1) y-(8.x² +4x² -1) by knowing u =x is a solution.

A: Given: dydx=-8xy2+4x4x+1y-8x3+4x2-1

Q: Rodrigues' Farmula (x²-1)! %3D 2L L! dx' Solve for Pg cx), P4 Cx), PEC

A:

Q: noose a non-exact equation and solve. (xy - 2y?)dx - (x2 - 3xy)dy=D0 1. 2)

A: Q(1)  We have to solve given non exact differential equation:

Q: a) Find the general solution of the equation dªy dy dx² 4- x2 + 3e* - dr4 by using the method of…

A: As you have posted multiple parts,but they are independent so according to our guidelines we will…

Q: Find solutions using Exact Equations 3. Solve e** (3x²y – x²)dx + e**dy = 0 |

A: Given that: ex3(3x2y-x2)dx+ex3dy=0

Q: Using undeterminate coefficien ts, Solve : d'y _q dy =9 e + 82* dx 3 3X 3 dx

A:

Q: Solve an exact equation?  M(x,y) + N(x,y)*dy/dx = 0

A: Given: M(x,y)+N(x,y)(dydx)=0

Q: Q.No.3: a) Solve Cauchy-Euler equation d'y 3x3 dx3 d²y dx2 dy + 9x? + 6х— — бу %3 1+x3 dx

A:

Q: dy 4у dx х (у-3)

A: Given query is to find the soly of the differential equation.

Q: (2x2y+3y3)dx - (x3+2xy2)dy = C Solve for Particular Solution when x = 1, y = 1

A:

Q: dy - 9 -2メ ーメe ニ 3 Il

A: The given differential equation is; dy/dx - y = -x e-2xy3

Q: z = xy dy x2+y= 2x/1-x’y² dx 2. Using the substitution ,change the to a separable equation. Hence…

A: We are given the differential equation  xdydx+y=2x1-x2y2 we have to use the substitution z=xy.

Q: 2. Obtain the general solution using Bernoulli's equation. Simplify your final answer. + x dx - –…

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

Q: Solve the Bernoulli equation. 3xy' + y = y¯8 x>

A: We have to solve

Q: dx -dy = 0 4. Solve

A:

Q: c). Using an integrating factor solve the equation dy , 4. +y= 3x dx

A:

Q: (8x² y² -2x + 4xy² - x) dx + (2xy + x + 2y + 1) dy = 0

A:

Q: (1 + y²) dx + (x²y + y) dy = 0.

A:

Q: 2. 2x5 = y(3x* + y²) %3D dx

A:

Q: dy %3| 6x5-2x+1 dx cos y+ey

A:

Q: Q5. Transfer the Cauchy-Euler equation to a constant coefficient equation and find the general…

A:

Q: 4. Solve dx - dy = 0 xy-1 xay

A:

Q: x2 dy dx2 d²y dy + 2y = 5x° cos(x) 2x Jx - dr solve the equation by undetermined coefficients method

A:

Q: FIND THE PARTICULAR SOLUTION: SHOW SOLUTION AND PROVE THAT THE EQUATION (y4-2xy)dx+3x2dy=0; when…

A: We have to find the solution

Q: y=x√3-2x³

A:

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

A:

Q: 2. Obtain the general solution using Bernoulli's equation. Simplify your final answer. 3 (2y° + x/…

A:

Q: 4. Solve dx - dy = xy-1 1 o = áp-

A:

Q: dy %3D dx = (9x + 4y + 1)?

A: The given equation is, dydx=9x+4y+12                     .........1 Let 9x+4y+1=v…

Q: b) Find the general solution of (3sin y– 5x)dx+2x² cot ydy = 0

A:

Q: 1. (5x + 4y) dx + (4x – 8y³) dy = -

A:

Q: Check for exactness and obtain the general solution. 1. -x(4y3 – 3xy – 6)dx – (6x²y² + 1- x³)dy = 0

A:

Q: xydx - (x^2+3y^2)dy =0 Solve for general solution .(show complete solution)

A: Given, xy dx - (x2+3y2) dy =0

Q: Solve the given DE using 3 methods/possible solutions: Attach your complete solutions & answers (2y3…

A:

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

A:

Q: Solve the diffrential equation.(pls step bu step and clearly) (d/dx+2x)(dy/dx+2xy)=2e^(-x^2)

A: We have given differential equation is…

Q: Obtain the general solution to the equation. * + 2x = 4y° dy The general solution is x(y) = |…

A: To obtain the general solution of the Linear Differential Equation

Q: Solve e (3x²y – x²)dx+ e*dy = 0

A:

Q: (2xy - x + 2y - 1) dx + (8x² y² -2x + 4xy2 - x) dy = 0

A:

Q: Using the substitution x= X -3 and y= Y-3 show that the equation dy y+3 dx x+y+6 can be reduced to a…

A:

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

A:

Q: Given (x² + 2y)dx + (+ 2xy+ 2x) dy = 0. 3 i) Check the exactness of the equation. ii) Based on your…

A:

Q: Solve the equations by variation of parameters. d2y/dx2 -dy/dx = ex cos x, x> 0

A: d2ydx2-dydx=excosx