Find the gcneral Solution 2. cdy - 3y = C di

Q: Let y(x) be the solution for the DE: y = (x + y-1)? If y(0)– 1, then find y() 3元 O 2+7 O8-7 O 2-7

A:

Q: y=c,J,(V3x) +c,J,(/3x)is solution for x?y "+xy'+ (9x² – 3)y=0 ylgn İhi

A: False

Q: ) Use the d'Alembert solution to solve = 2 -00 0, 1 u(x, 0) = e, u(x, 0) : 1+ x2*

A: As per our company guidline we are supposed to answer only first question. Kindly repost other…

Q: -2X O y- 2y'ty = e5x %3D aut put di fferential equo tion below pereral solution the

A:

Q: Solve the DE. If o(x) is the solution to the DE, find o( - 2) $( – y = xe- x*: (0) = 0

A: Solution of the differential equation

Q: y" + 5y/ + 4y = 4te*.

A:

Q: 6. Find the particular solution of ydx – 4xdy = y6dy; where x = 4 and y = 1.

A:

Q: Let y(x) be the solution for the DE : y' = (x + y – 1)² If y(0) = 1, then find y()

A:

Q: find the particular solution to y’’ + 5y’ − 6y  =  6t + 7

A: y"+5y'-6y=6t+7Auxillary eq f(D)=D2-5D-6Q = 6t+7Particular Integral be denoted by…

Q: Find the solution. y'• ty ty" © y- (1-c, y- - (1-co")

A: We have to solve y'+ty=ty3 This can be written as: y'+ty=ty3⇒1y3y'+tyy3=t⇒1y3y'+ty2=t⇒1y3dydt+ty2=t…

Q: Let y(x) be the solution for the DE : y = (x + y + 2)2 If y(0) = -2, then find y() ○2-푸 O 8 - T O -…

A:

Q: rydc+(2x2+3y2-20)dy=0

A: Given DE is xy dx+2x2+3y2-20dy=0 solve the given DE

Q: The solution of y' e'+V is e-Y = - e'+ c Select one: True O False xam

A:

Q: The general solution of : y' = y In(y) Select one: O a. y= e*+c O b. y= elnx + c C. y =c ex O d. y =…

A: Given differential equation is first order variable separable differential equation. To solve the…

Q: Solve by VP: y"' – 3y" + 2y' - et 1+e-x

A:

Q: Consider the IVP: y" + 9y = 40ex ; y(0) = 5, y'(0) = -2. Find the general solution.

A:

Q: Let y(x) be the solution for the DE: y (x + y +2)² If y(0) = -2, then find y() 7- 3 4 2+ O 8 JTO 3…

A:

Q: What values of z and A make y=Acos(zt) a solution to y''+3y=0 such that y'(1)=1

A:

Q: A. Determine the solution set of the following equations using variable separable. 2. y' = xy? %3D

A:

Q: Solve the given IVP: y" + 7y" + 33y' – 41y = 0; y(0) = 1, y'(0) = 2, y"(0) = 4.

A: The given initial value problem is                                      y'''+7y''+33y'-41y=0 ;…

Q: The general solution of the DE x?y" + xy' – 9y = 0 where y(1) = 2 and y'(1) = 0 is %3D

A: Given differential equation: x2y''+xy'-9y=0 wherey1=2 and y'1=0

Q: 03) Prove or disprove that y = ce* + de ²x is the solution to y(2) + y(¹) - 2y = 0.

A:

Q: Find a particular solution to y′′+16y=24sin(4t).

A:

Q: For what value ofk the linear Diophantine equation 21x + 14y = k has solution a) k = 1 b) k = 36 c)…

A:

Q: The solution of DE.s divided into complementary solution and particular solution. * O True False

A: Consider a nth order differential equation dnydxn+dn-1ydxn-1+dn-2ydxn-2+.........................+y…

Q: Find a particular solution to y′′+5y′+4y=15te^2t

A: We find a particular solution to y′′+5y′+4y=15te2t.

Q: Find a particular solution to y′′+36y=24sec(6t). yp=

A: Find the roots of the auxiliary equation and then assume it as shown in step2

Q: Find a particular solution to y" + 5y' + 6y = 18te. Yp =

A: G

Q: Find a particular solution to y′′+36y=60sin(6t) yp=

A: The given differential equation is  To calculate the particular integral let us consider If we put…

Q: The general solution of: y' =y In(y) Select one: a. O b. C. O d. V =cex

A:

Q: What values of α and A make y=Acos⁡αt a solution to y″+2y=0 such that y′(1)=3? α= A=

A: We have to find value of a and A.

Q: Find the general solution of the given second-order rerential eque 5y" + y = 0 y(x) = %3D

A:

Q: If y, =e", y2 =te are solutions to y"+b y' +c y = 0, find the values of b and c.

A: Given: y''+by'+cy=0y1=e4t ,y2=te4t

Q: Find the value of y, for wich the solution of the I.V.P y' - y =1+3sin t, y(0) = yo remains finite…

A: Here we are given an I.V.P                                         y'-y=1+3sint Also it is given…

Q: What values of α and A make y=Acos(αt) a solution to y′′+6y=0 such that y′(1)=2?

A: The solution of differential equation y’’+6y=0 is

Q: For what value(s) of k will y 1 be a solution of ty" + (t – 3)y' + ky = 2te¬2t? e2t

A:

Q: The general solution of : y' y In(y) Select one: O a. y=ee*+c O b. y = c ex C. V3ex+c

A:

Q: Find two values of n such that y = enI is a solution of y" + y' – 72y = 0

A: Given differential equation,  y'' + y' -72y = 0 To find the solution of above equation in form of…

Q: Given the IVP: y/" – 7y' + 6y = 8, y(0) = 0, y'(0) = 1. %3D Find the solution of the above IVP.

A: Solution

Q: z Solve the following di fferential equations xdy y x²+y² 1. dy

A:

Q: A particular solution of y - 2y +y = e': | Select one: а. Ae b. Ate' С. At?e' d. At³e

A: Given differential equation is  y" - 2y' + y = et

Q: 7. Find the solution of y' -= a. y = ce x - 3 y = ce*+; — се х 3 с. у%3D сех 3. d. y = 1 — сех +. 3…

A:

Q: Find the goneral solution: 5. H.W auswer! Xe.

A:

Q: Solve for y. P(0)=(-12/37, y), P(0) is in Ql

A: Given P(θ)=-1237, y and P(θ) is in Quadrant 2.

Q: Obtain the particular solution of (3x² – 2y²)y' = 2xy when x = 0,y = 1. a. x2 = 2y² (y + 1) c. x2 =…

A: Let's find.

Q: 3. Find a second solution to y" – 25y = 0, given one solution y1(x) = e5z. %3D %3D

A: Given differential equation is y''-25y=0 & y1x=e5x be one solution of the differential equation.…

Q: 'ind the general solution of d³y 6. dr3 dy - 8y = 21e2 dr dr2

A:

Q: The solution of the IVP y" + 9y=0, y(0) = 1, y'(o) = 0, is %3D

A:

Q: 2) Gr. Find a solution for the BVP: y" + 49y = 0, y'(0) = -3 and y') = 3. %3D

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.