Which of the following equations can be reduced to the homogenuous linear differential equation with constant coefficient? O a. dy 32. da? da 0 = 32. 3 dy = 0 da3 da 3 dy 2 dy da? da? da O d. a d'y dy dy da? da O e. dy da2 da ||

Q: 40. Let y = 3x? - 2x + 1. Use differentials to find the ap- proximate change in y when x = 2 and Ax…

A: Consider the function y=3x2-2x+1. Need to find the approximate change in y when x=2 and ∆x=0.05.

Q: solve D.E. by using separable of variable dy 1 V2xy dx

A:

Q: 3. Obtain the homogeneous linear equation satisfied by the following function. y = x² Sinx + e5x

A:

Q: (2y3 – x³)dx + 3xy?dy = 0; when x = 1, y = 1 Ans. 5x²y3 = x5 + 4

A:

Q: Which one is the equation corresponding to the differential operator (D – 2)(D+ 2) when the operator…

A: Given differential operator is  D-2D+2

Q: Solve the following Bernoulli equation: dy - 4y-2y dx

A: We have to do variable separation.

Q: dy 4у dx х (у-3)

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

Q: The order of the following differential equation (x² +v²)xy Select one: a. 4 b. 1 с. 2 d. 0

A:

Q: what is the differential of z Sy +7y + 6y- 8y? Ode (2-2y 12y+3) dy ৯ ( ) O dy- (2 2 12y) de O42…

A: We can solve it properly to get the required differential as below

Q: Indicate whether the following statement is true or false. The change of variable formula reads:…

A: We have to check whether the statement, "∬Dfx,ydxdy=∬D'fxu,v,yu,v∂x,y∂u,vdudv" is true or false. The…

Q: Determine dy if y=2e +3 da dy da = HP

A:

Q: 2. Determine dy/dx of the following equation. y = a. C. eeez dy dx = dy dx eeez = e. None of the…

A:

Q: d³y – 3 – 18y = 0 dx³ dx² dx

A: Write the corresponding auxiliary equation of the given differential equation y"'+4y"-3y'-18y= 0

Q: For which value of r is y = et a solution of the differential equation 2- 3y = 0? %3D a. -3 b. 0 d.…

A:

Q: Find an expression for dy/dx. y = u? and u = 3x - 1 18x 18x - 6 0 9x -3 O 6x - 3

A:

Q: p= I.F. = e/P(x) dx Now solve (I.F.) y = f (I.F.) - Q(x) dx 9. Solve the linear ODE using an…

A:

Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.