Find the particular solution of the given higher-order differential equation. y''' + 2y'' - 5y' - 6 = 0; y(0) = y'(0) = 0, y''(0) = 1

Q: Find the general solution of the given higher-order differential equation. y"" + 4y" - 9y' - 36y = 0

A: Follow the procedure given below.

Q: 4. The Bernoulli's form of the differential equation x'dy+ (2xy-y')dx=0 is

A: Given problem:- The Bernoulli's form of the differential equation x2 dy + (2xy - y3)dx = 0

Q: In the given equation , find the particular solution of the first-order linear differential equation…

A: We have  given first order linear differential equation y'+2x-1y=0 Let P=2x-1 and Q=0 Then,…

Q: For the differential equation x-4y"-2y'+y 0, the point x = -2 is Select the correct answer.

A: One distinguishes the following cases: Point a is an ordinary point when functions p1(x) and p0(x)…

Q: Find the general solution of the reducible second-order differential equation: x²y" + 3xy' = 2

A: To find the general solution of the second order differential equation

Q: Find the general solution of the given second-order differential equation. 6y" + y = 0

A: To find the general solution of  6y''+y=0

Q: Find the general solution of the given second-order differential equation. 3y" + y' = 0 y(x) =

A: Given second order differential equation is 3y"+y'=0.

Q: Find the general solution of the first-order linear differential equation. xy' + y = x³3 + 1

A:

Q: Find the general solution of the given higher-order differential equation. y"" - 2y" - 3y' = 0 y(x)…

A:

Q: 7. Find the particular solution of the differential equation dx +5x³y x³ passing through the point

A: Given, dydx+5x3y=x3,   0,72 it is a linear differential equation p(x)=5x3,  q(x)=x3…

Q: The particular solution of the following nonhomogeneous differential equation y"-2y' +y = x² +e-* by…

A: Given nonhomogeneous differential equation:y"- 2y'+ y= x2 + e(-x)  ;

Q: Find the general solution of the given second-order differential equation. 6y"+y' = 0

A:

Q: Find the General solution of the homogenous differential equation: y"-6y'+9y=0

A: We need to find the General solution of the homogenous differential equation y''-6y'+9y=0.

Q: Find the general solution of the first-order differential equation                     (x + y) dx −…

A: To Determine: Find the general solution of the first-order differential equation by any appropriate…

Q: Given the differential equation and its initial conditions y" - y' 2y 0 with y(0) = -2 and y'(0) = 5

A:

Q: What is the general solution to the the differential equation3y"'-y' - 2y=0?

A:

Q: What is the solution of the first order differential equation y(k + 1) = y(k) + 5.

A:

Q: Find the general solution of the first-order linear differential equation y′ + 2xy = 10x for x >…

A: Given y'+2xy=10x

Q: Find the general solution of the given higher-order differential equation. у" - 2у" — Зy' — 0 y(x) =

A:

Q: Find the general solution of the given higher-order differential equation. y(4) + y''' + y'' = 0…

A: The given differentail equation is  y(4) + y′″ + y″ = 0.

Q: 2. y-폼-y 1 ミ、 6x 3x2 ||

A:

Q: Find the particular solution of the first-order linear differential equation        y′ + y = 6ex…

A: y'+y=6ex Comparing with y'+Py=Q, we get P=1 & Q=6ex Now the integrating factor is, IF=e∫P dx=e∫1…

Q: Find the general solution of the given second-order differential equation. 3y" + 2y' + y = 0 y(x) =

A: We need to find general solution.

Q: Find the general solution of the reducible second-order differential equation x?y" + 3xy' = 2

A:

Q: Determine the appropriate form for yp on the differential equation y" = 9x^2 + 2x - 1 %3D

A:

Q: Find the solution of the first order differential equation with the given initial condition: y…

A:

Q: Find the general solution of the first-order differential equation                    (2y − ex) dx +…

A: Given first order differential equation is 2y-exdx+xdy=0 for x>0. To find the general solution.…

Q: Find the general solution of the given second-order differential equation. 9y"+y' = 0 y(x) =

A: General solution of real roots is used.

Q: find the general solution of the first-order linear differential equation. 3xy' − y = x−1

A:

Q: 2.Form the differential equation from the family of curves y² = Ae³* + Be* , where A and B are…

A:

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

A:

Q: Find the general solution of the given second-order differential equation. y" + 4y = 0 y(x) =

A:

Q: Find the value of y for the given differential equation if the value of the arbitrary constants is…

A:

Q: Solve the differential equation with initial conditions y" - 3y 10y = 4e5t y(0) = 0, y' (0) = 1…

A:

Q: The particular solution of the following nonhomogeneous differential equation y" – 2y' + y = 4x² +…

A: y''-2y'+y=4x2+ex This has characteristic equation               λ2-2λ+1=0λ-12=0λ=1…

Q: Find the general solution of the given second-order differential equation. y" + 9y = 0 y(x) =

A: Given equation, y''+9y=0 It can be written as, (D2+9)y(x)=0, where D=ddx

Q: Find the general solution of the given second-order differential equation. 3y"+y' = 0 y(x) = =

A: To find out the general solution of the given differential equation.

Q: What is the particular solution of the differential equation determined by the initial conditions,…

A: In the question we have to find the particular solution.

Q: Find the general solution of the given second-order differential equation. y" - y' - 20y = 0

A:

Q: The particular solution of the following nonhomogeneous differential equation y" - y' - 2y = 4x² +e*…

A: Here  Particular solution is in the form  yp(x) = Ax2 + Bx + C + De-x

Q: Find the general solution of the given higher-order differential equation. y""8y" - 9y' = 0 y(x) =

A:

Q: Find the general solution of the first-order linear differential equation y′ + 3x2y = 6x2 for x >…

A: Given: The first-order linear differential equation: y'+3x2y=6x2 for x>0.

Q: Find the general solution of the given second-order differential equation. 3y" + y = 0 y(x) = ||

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

Q: 3. The Bernoulli's form of the differential equation x³ydx+(3x¹-y³dy=0 is

A:

Q: The general solution of the fifth-order differential equation y(5) + 4y(3) = 0. is:

A:

Q: Find the general solution of the given second-order differential equation. y" - y' 20y = 0 y(x) =

A:

Q: Find the general solution of the given higher-order differential equation. y" - 2y" - 3y' = 0 y(x) =

A:

Q: 2. | Determine the general solution of the given differential equation y" -6y" = 3- cos x

A: The solution is given as

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.