a) Find the value of 2, for which the following differential equation will be an exact DE:

Q: 2. Find the general solution of the given differential equation. dr + rsece = cos0 do

A: The given differential equation is; dr/d(theta) + r sec(theta)=cos(theta).

Q: Solve the following differential equations of -cos(y)·y'+sin(y)=x Linear Differential Equation

A: Let's find.

Q: 3. Solve this differential equation, using T(0) = To as initial condition. %3D

A:

Q: ( + cos

A: We use exact differential equation to solve this ODE.

Q: Solve the following differential equations : (A) xy' = - In

A:

Q: Determine the integrating factors in each of the following differential equations and solve for the…

A: A detailed solution is given below.

Q: Identify the auxiliary equation of the following differential equation along with its roots and the…

A: Given differential equation is second order linear homogeneous differential equation: y''+6y'+8y=0…

Q: solve the following differential equations using the substitution suggested by the equation.

A:

Q: Solve the following ordinary differential equation y"+7e%y'+y=sinx

A:

Q: х dx + 3xydx = 0 хdу — 2ydy

A:

Q: Solve the following differential equation using MVP * y"+ y'= tan t

A:

Q: dy

A: Consider the given differential equation. ex1+dydx=xe-y This is separable differentiable equation.…

Q: 4. y = Cie+ C2e + Cse, where y(0) =0, y'(0) = 1, y"(0) = 2 %3D

A:

Q: Solve the following Bernoulli's differential equation. y'+tany = e ,7x = e^.secy.

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

Q: Iny = Aex + Bex %3D

A:

Q: 1. y' + 52 = x² + 1 %3D

A:

Q: dy dr = cos(²) +

A:

Q: 2

A:

Q: 6. yi+ yž = 1, when x = 0, y = 4 dx

A:

Q: dy ar + by dr br + cy

A: Given exact differential equation is

Q: e dy

A:

Q: у %3D Сјех + С2xe* + Сзех + 2x?ex

A:

Q: Solve the given differential equation by using an appropriate substitution. The DE is a Bernoulli…

A: Given that the differential equation is     x(dy/dx) + y = 1/y2

Q: In the given question as follows , find the general solution of the differential equation using any…

A: To find the general solution of the differential equation: y'=1-cosθ Solution: We have formula,…

Q: Solve the following differential equation using appropriate method. 3. (r+ sine - cose) dr + r(sine+…

A: r+sinθ-cosθdr+rsinθ+cosθdθ=0

Q: Consider the following differential equation f + = cos (x) What is the general solution ?

A:

Q: Apply the Euler method to solving the following differential equation with the given parameters. y'…

A: option(5) is correct.

Q: Solve the following differential equations using the method for exact equations.

A:

Q: y = C1 e2x c cos 3x + c2 e2* sin 3x

A: The general solution is given as , y=c1e2xcos3x+c2e2xsin3x find differential equation.

Q: Solve the given differential equation. (Hint: Bernoulli) y' + y = y?

A:

Q: у" — бу' — 7у%3D11 sin 4x -

A: We have to mention the general form of the particular solution

Q: xdy-ydr =xy²dx %3D

A:

Q: y = Aeax cosbx + Beax sinbx where a and b are parameters

A: Proceed as shown

Q: (3x²+ 2y²)dx + 2xydy=0

A: According to guidelines here solution of only firt question

Q: Solve the following differential equations by finding integrating factor dy --y = e2x dx

A: We need to solve the given differential equation using integrating factor method.

Q: a sin a + In v ) da + tan adv = 0 COs a

A:

Q: Determine the integrating factors of the following differential equations and solve for the general…

A: The objective is to determine the integrating factors of the following differential equation and…

Q: Solve the given differential equation by using an appropriate substitution. The DE is a Bernoulli…

A: The solution is given in the next step.

Q: Solve the following given differential equation  using the method of indeterminate coefficients

A:

Q: Solve the given differential equation by finding, in-imanapi 12xy dx + (4y + 18x²) dy = 0 Sectioner,…

A:

Q: siny ( x + sin y ) dx + 2x² cosydy %3D

A:

Q: Which of the following differential equation has a solution of In(y) = G e* + C2e*

A:

Q: Solve the following Exact/Inexact Differential Equations. If it is inexact solve it by finding the…

A:

Q: (2³ + y³)dx + 3xy°dy =

A:

Q: Obtain the solution on the following differential equations:

A:

Q: Solve the following differential equations. Use the method of Bernoulli's Equation.

A: Solution Given y2dy-(4y3+48x)dx=0We need to solve the differential equations.by using the method of…

Q: Solve the given differential equation by using an appropriate substitution. The DE is a Bernoulli…

A: Introduction: An equation of the form y'+ p(x) y=q(x) yn is the Bernoulli differential equation.…

Q: : Find the general solution for the following differential equations:

A:

Q: dy dr 3 = e*y*

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.