1. y = c1e-2x + cze²x + cze2x 2. y = c1e* + cze3x

Q: Find the particular solution for the differential equation y' = 4xe2x and y(0)=20.

A:

Q: It is known that h1(t)=e3t2, h2(t)=30e3t2 are solutions of the differential equation 4h" - 12h' + bh…

A:

Q: Given the solution:  y = C1e-2x + C2e2x + x2  Which differential equation is it a solution of?

A:

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: Formulate a differential equation that is satisfied by 1. y=Ae2+ Bxe2x 2x + Bxe2x

A: The given equation is: y=Ae2x+Bxe2x Formulate a differential equation that is satisfied by the given…

Q: Show that the differential equation  (2xy3 - 3y2 + 2xy2)dx + (3x2y2 - 6xy + 2x2y)dy = 0 is exact and…

A: To show that the differential equation  2xy3-3y2+2xy2dx+3x2y2-6xy+2x2ydy=0 is exact and to find its…

Q: 7. 2yy = e-: y(4) =-2

A:

Q: Which of the options is the differential equation that accepts the solution of the following…

A:

Q: Find a differential equation whose general solution is y = C₁e6t + c₂e-4t y" - 2 y' - 24 = 0 X

A: The solution of the DE is: y=c1e6t+c2e-4t where the solutions to the auxiliary equation are 6 &…

Q: 3. Find the differential equation associated to the equation: y = C₁x²e³* +C₁xe¹ +C₁e¹*

A: Note:- Since you asked multiple Questions ,As per our policy we can solve first question  for you…

Q: The general solution of the differential equation 81.x² y" + 81xy' + (81x² – 25)y = 0 is? Check all…

A:

Q: Find a differential equation whose general solution is y = c₁e³t+c₂e-3t 5t = 0

A: The general solution,y=c1e5t+c2e-3t

Q: Find the general solution of the differential equation (x³+xy²) y' =y8.

A: We have to find the general solution of the differential equation x3+xy2y'=y3

Q: 3. Find the differential equation associated to the equation: Y = C₁xe¹³ +₂e=³ +C₁x²e-³

A:

Q: Find the particular solution of each differential equation that satisfies the initial condition.…

A: The given differential equation is: y'-8x3y=e2x4;       y(0)=2

Q: What is the general solution to the the differential equation3y" - y'- 2y = 10e *?

A:

Q: 4.Determine if the given function is a solution of the given differential equation

A:

Q: Find the differential equation that has y = C1 + C2x as its general solution.

A: To find the original differential equation we  have to eleminate the arbitrary constants by…

Q: Find a differential equation whose general solution is y = c₁e³t+c₂e-2t 2 = 0

A: We need to determine a differential equation corresponding to the general solution: y=c1e5t+c2e-2t.

Q: Determine the form of a particular solution for each differential equation 2 2. ""4" +4y' = 5x² - 2x…

A:

Q: Find the particular solution for the differential equation y' 4xe2x and y(0) =20.

A: Given that a differential equation and we find its particular solution . and also given that a…

Q: 4. Identify whether y' - 3y = 6 is a linear differential equation or a Bernoulli equation, and solve…

A:

Q: The equation x² + e¤y = c defines an implicit solution of the differential equation

A: We have to differentiate the given equation with respect to x first.

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

A:

Q: Determine the form of a particular solution for each differential equation. y'' - 2y' + y =…

A: We have to determine the form of a particular solution for each differential equation.…

Q: 5. Find the general solution of the differential equation y=(2y4+2x)y'.

A: Given differentiatial equation: y = (2y^4+2x)y'  Here y'= dy/dx

Q: (b) Find the complete solution of the differential equation y" + 9y = -5x² + 4cos2x

A:

Q: 2x³y' = y(y² + 3x?)

A:

Q: What is the solution of the following differential equation that satisfies y (1) = 7 and y '(2) = 3?…

A:

Q: Find the general solution of the differential equation 2xyy' = 2y² – x²

A: given 2xy y' = 2y' -x'y' = 2y2-x22xy---(1)put y =vxy' = v + xv'---(2)so from (!) we have y' =…

Q: 5. Find the solution of the differential equation using Variation of Parameters. у" - Зу" + Зу 3 E

A: Given y'''-3y''+3y'=exx

Q: Formulate a differential equation that is satisfied by 1. y=Ae2+ Bxe²r

A: To find: The differential equation: Given: The equation is y=Ae2x+Bxe2x. Concept used: Product rule:…

Q: 13.Find a differential equation whose general solution is y = c1e2t + c2e−3t.

A: The given solution is y= c1e2t+c2e−3t.

Q: Find a differential equation whose general solution is 9t y = c₁e⁹t + c₂e-²t = 0

A:

Q: Find the general solution of the differential equation. y' = 21x y

A: The differential equation is given by y' = 21xy To evaluate : The general solution of the…

Q: Find a differential equation whose general solution is 7t y = c₁e¹t + c₂e-2t. y" - 5 y' - 14 y = 0 ✓

A:

Q: 1.3x – xy = c -

A:

Q: Find a differential equation whose general solution is 9t = C₁e⁹t + c₂e-5t. y = = 0

A:

Q: y = cje* + cze²r y" -y – 2y = 0 O 2y " -y' – y = 0

A:

Q: verify that given situation is solution of the differential equation. y' + 4xy = 0, y = 25e−2x2

A:

Q: Eliminate the arbitrary constants to find the differential equation y = C¡e¬* – C2e-2x + Cze-3x

A:

Q: Find a differential equation whose general solution is y = c₁e5t + c₂e-²t. = 0

A:

Q: Find a differential equation whose general solution is 7t y = c₁e²t + c₂e-5t = 0

A:

Q: Find the solution of the following Differential Equations by homogenous equation 7) y'=(y-x)

A: Since you have asked multiple questions, we will solve the first question for you. If you want any…

Q: (1+ x)y" + (4x + 5)y' + (4x + 6)y = e-2x

A:

Q: Write down the solution of the differential equation: x² y" -4 y' + 4y = In x

A: Consider the expression lnx as t. Differentiate the equation t=lnx and simplify to obtain the…

Q: (b) Discuss the complete solution of the differential equation y" + 9y = -5x² + 4cos2x

A:

Q: What is the solution to the equation for the differential equation x^(2)y''+3xy'+y=0

A: The given problem is to solve the given differential equation , the given differential equation is…

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.