10. (a) Show that the differential equation (4x + 3y?) dx + 2xy dy = 0 is not exact. (b) Find an integrating factor of the form ", where n is a positivc integer. (c) Multiply thc DE through by the integrat- ing factor found in part (b) and solve the resulting exact cquation.

Q: Solve the differential equation f -e = 2ey by separation of variables.

A: In this question, concept of separation of variables is used. Seperation of Variables The approach…

Q: Q. Find general Solution of the differential equation

A: We need to solve t2y''+3ty'-3y=t-1 We use Cauchy Euler equation to solve this: Let t=ez  ⇒z=logt…

Q: Solve the following differential equation: ydx + rdy + xdx 0. 1- 2?y2

A: Solution is in step 2

Q: Solve the differential equation defined by x dy/dx −2y = x^6 sinx.

A: Consider the provided differential equation,

Q: Solve the differential equation by variation of parameteres:   y'' + y = sin2 (x)

A:

Q: Detemine whether the differential equation is linegror non liner and give reasons. O54y +Siny=

A:

Q: Form the differential equation of family of lines situated at a constant distance p from the origin.

A: Since you have posted a multiple question according to guildlines I will solve first question for…

Q: Solve the differential equation using Bernoulli equation xy' - y = xkyn

A:

Q: Solve the differential equation by variation of parameteres: 4y'' - y = ex/2  +7

A:

Q: find the degree of the differential equation y''-12cosec y= 0   3 1 4 or 2

A: The order of the differential equation is 2.

Q: The differential equation 4y"- siny y' + 3y = O is a linear equation. :Select one True False

A:

Q: Solve the differential equation by variation of parameters. y" + y = sec(8) tan(0) y(8) =

A:

Q: Derive a Differential Equation that is free from arbitrary constants: y = C₁x + C₂e*

A: