What is the integrating factor of the given differential equation? 3 3 (2y – xHdx + 3x²ýdy = 0 А. у? В. х-2 C. x² D. None of the above

Q: 7. Consider the differential equation dy -t y° . dt (a) Solve the initial value problem with y(0) =…

A:

Q: 5. For what values of r does the function y = e™* satisfy the differential equation 2y" + y' – y =…

A: Given , differential equation       2y" + y' - y = 0   (2D2 + D - 1)y = 0 The auxiliary equation of…

Q: Select the general solution to-the differential equation: y = 3x y 1 y = Vx3 + C y = e3z3 y = Cez 1…

A: Given Differebtial Equation,  y'=3x2y dydx=3x2y

Q: Find the general solution of the given differential equation. x2(dy/dx) + x(x+2)y = ex Determine…

A: The differential equation is x2(dy/dx) + x ( x + 2) y =ex.

Q: 4. Eliminate the arbitrary constant 'a' in the differential equation: y – 2ay' + x2 = a? %3D

A:

Q: Q3/ Choose two only a. if y - asin3x + bcos3x satisfies the differential equation + 4 + 3y =…

A:

Q: 1 3. y' -- %3D xy+x²y3

A: See the details solution in below

Q: For what values of r does the function y= e™* satisfy the differential equation y"- 4y'+ 2y = 0?

A: for the homogeneous differential equation, the auxiliary equation is  compare this equation with…

Q: use the method of variation of parameters to determine the general solution of the given…

A:

Q: 2x-y? xy? 3- ()dr – ()dy = 0 is exact differential equation. True False o o

A:

Q: 1. ax дхду?, 2. dy + 2x+ y = x² + 2 3. дхду = y

A: Due to our guidelines, we can solve only three subparts plzz reupload rest question by mentioning it…

Q: By solving the differential equation: y = (x − 8)y' + (y′) ³³ 33 It is obtained, as part of its…

A: Consider the given differential equation, y=x-8y'+y'33 Since, it is given that as a part of its…

Q: 5. Find the general solution to the differential equation et y" – 2y' + y 1+ x2 (where y' = )

A: Let us consider the differential equation y''+py'+q=g(x) To solve the equation  Determine the…

Q: Find the general solution of the first-order linear differential equation. e2x y' = 4 – e*y (Express…

A:

Q: 8. Consider the homogeneous linear equation: 2.a²y" + 3xy' – y = 0, x > 0. (a) Explain why y = e" is…

A: Note: Since these are independent subparts, according to our policy we are only allowed to solve…

Q: 7. Consider the differential equation dy yt 1+t dt (a) Solve the initial value problem with y(1) =1.…

A: Solve the given problem.

Q: Find the general solution of the given higher-order differential equation. du + + 6- drs dr4 12- dr2…

A:

Q: 4(3х + у — 2)dx — (3х + у)dy %3D 0 -

A:

Q: Suppose the auxiliary equation of a homogeneous linear differential equation has roots m_1=-2 and…

A: We have given the root of the auxiliary equation which is m1=2 and m2=+-2i

Q: 2. Solve the differential equation (3.x² – x³ + 3y – 3.xy – y³)dx + 3(x + y²)dy= 0, - by determining…

A: Exact differential equations solved by using integrating factor

Q: What is the value of k that will make the differential equation (6x + y) da + y (kz -3y) dy =0 exact…

A:

Q: What is the particular solution to the differential equation - xy? with the initial condition y (2)…

A:

Q: 4) In the differential equation of, y(x³ – y)dx – x(x³ + y)dy = 0 - where a and ß are constants,…

A: Explanation of the solution is given below....

Q: Let the following higher order differential equation y" – 2 y" – 3 y' = 3e5z (1). Determine the…

A: Consider the given information: y'''-2y''-3y'=3e5x To find the general solution by variation of…

Q: 2. Solve the nonhomogeneous differential equation, using the basic rule: y(2) + 6y(1) + 9y =…

A:

Q: ds What is the general solution to the differential equation 2 = 5t's³? %3D dt

A:

Q: The differential equation y' – y = 0 has a solution of 1 y(x) = n! n=0 Show v(r) is a soluution to…

A:

Q: y² = Ax² + B sec x

A: Given equation: y2=Ax2+BsecxTo find: General solution by eliminating all the arbitrary…

Q: Eliminate the arbitrary constants in the equation defined by y = ae^(3x) + bxe^(3x). Which of the…

A:

Q: y = c1 e(-2+v3)x + c» + c2 e(-2-v/3) z

A:

Q: 4. (4D2 + 4D + 1)y = 7e-* + 2 when y(0) = 1; y'(0) = 3

A:

Q: Solve the differential equation (21xy + 21y²) + (7x² +21xy) y = 0 using the integrating factor u(x,…

A: Given : A differential equation (21xy+21y2)+(7x2+21xy)y'=0. The integrating factor is…

Q: 4.Calculate the differential equation y''= 3x + y2 + y + y', y (0) = 2, y (1) = 4 by shoot-ing /…

A: Given that the differential equation is  y''=3x+y2+y+y'; y(0)=2, y(1)=4 Also given that h=1/3 we…

Q: 2- Find the solution of these differential equations : 1. (x – y) = x + y dy dr

A:

Q: Determine the solution to the initial value differential equation y'+ 8 y2 e4 x 0, y (0) = 9 y (x)…

A:

Q: A. Obtain the differential equation of the given solution by eliminating the arbitrary constant(s):…

A:

Q: 4. Use separation of variables to find the general solution of the differential equation. dy = 5t+1…

A:

Q: 8 Find the general solution of the differential equation: xy' + y: X Use lower case c for constant…

A: Given : xy'+y=8x+9x Following formulas are used- ∫1xdx=lnx∫xndx=xn+1  n+1

Q: What is the particular solution of the differential equation y" + 2y" – 5y' – 6y = 5e?? Particular…

A:

Q: 2. Solve the differential equation (3x² – a³ + 3y – 3ry – y*)dx + 3(x + y²)dy = 0, by determining an…

A:

Q: 6.Solve the linear differential equation for general solution

A: Let, The characteristic equation of the given differential equation is,…

Q: Solve for the particular solution of the non-homogeneous differential equation. 1. y'''+y''=3

A:

Q: Find the general solution of the given differential equations. y" – y' – 2y = cosh(2x)

A:

Q: Find the general solution of the higher order linear ordinary differential equation: y"' + 2y" + 4'…

A: We have to find general solution of given differential equation.

Q: Find the general solution of differential equation, and when initial conditios are given, the…

A:

Q: Show that the differential equation x¹y³ + x(1+y¹)y' = 0 is not exact, but becomes exact when…

A:

Q: Use separation of variables to find the general solution of the differential equation. e*(y' + + 3)…

A:

Q: 4. Use separation of variables to find the general solution of the differential equation. dy = 5t*…

A: