PART A: State the Order and Degree of each of the following differential equation and verify corresponding solutions. d²y = xsinx ; dx2 y = -2cosx – xsinx + cx + c2

Q: Find the differential equation whose solutions correspond to the following equation 1. y = C,e¬* +…

A: Apologies. We only answer one question at a time. We will answer question 1 as the exact one wasn't…

Q: y' - y = xe". a²y'+ay+2= 0.

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

Q: Q2/ Solve the following differential equation :- x?y" – 2xy' + 2y = xlnx, y(1) = 1: y'(1) = 0

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Q: Q5A: Find the solution of differential equation y" + y = sin(x). %3D

A: The complete solution of a differential equation contains a complementary function and a particular…

Q: Solve the following differential equation

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Q: Find the general solution for each differential equation.

A: we have to find the general solution of the given differential equation. dydx+2xy=4x

Q: Find a second solution of each differential equation. (1+ x)y" + xy' - y = 0; y1 = x.

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Q: Q3/Solve the differential equation 2dy + 5 = e2xsinx )

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Q: Solve for the differential equation of the given solution 2. y = C1xe* + C2e¬3x

A: We are given: y=C1xex+C2e-3x We need to find the differential equation for the given solution y.…

Q: (D² + 1)y = sec² x csc x

A: Solve the differential equation by the method of variation of parameters : D2+1y=sec2xcscx

Q: Solve the following differential equation step by step! y" – 2y' + y = x² + 1

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Q: Q3) Solve the following differential equation y" - y" - 4 y' - 6 0

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Q: Which of the following,functions are solutions of the differential equation y-3y 6? (c) y=e-2, (d)…

A: To Determine: which of the following functions are solutions of the differential equation? Given: we…

Q: Find the differential equation having each equation as general solution. m y ==-7

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Q: Find the differential equation whose solutions correspond to the following equation. y = C1x^2 +…

A: For the solution follow the next step.

Q: show that each function y = ƒ(x) is a solution of theaccompanying differential equation. y' = y2 y =…

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Q: Find the differential equation whose general solution is y = c1 x + c2 e

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Q: a. y = C,e=x + Cze-2x + x

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Q: Q2: Solve the following linear differential equation: y' + y = x+

A: We can solve this as follows:

Q: 2x³y' = y (y² + 3x²)

A: Topic = Differential equation

Q: Find the differential equation having the solution as: a. y = C,e¬x + C2e¬2x + x b. y = C, + C2e³x

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Q: PART A: State the Order and Degree of each of the following differential equation and verify…

A: the order of a DE is equal to the highest differential coefficient that it contains so in our case…

Q: Find the differential equation whoce is y= C1e-1% + solution = Czc-9x. + C2e 6x

A: A differential equation is an equation that involves derivatives or differential coefficients or…

Q: d) Solve the differential equation of y"" + 4y' = sec 2x

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Q: Solve the given differential equation by undetermined coefficients. y'' + 6y' + 9y = -xe4x

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Q: 8. x csc ) - y] dæ + xdy = 0

A: Given the differential equation

Q: Find the solution, using variation of parameters, to the differential equation (D3+D)y = sec2x.

A: Given :- The given differential equation is  D3 +Dy = sec2x Let the equation be  d2ydx2 +Pdydx+ Qy…

Q: Solve The Differential Equation Step by Step 4t²x" + (t²+1)x=0

A: Given differential equation is 4t2x''+(t2+1)x=0         (1) Let the solution be x=∑antn+m Then…

Q: If the differential equation y = 3px+ 6p°y? while solving for x takes the form x = then f(y,p) = (a)…

A: Giveny=3px+6p2y2x=f(y,p)To find f(y,p)

Q: Q2A: Find the general solution of homogenous differential equation xdy- ydx = x2 + y?dx. %3D

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Q: Find the differential equation whose solutions correspond to the following equation a. y= Cje*+ Czex…

A: Compare the solution of second degree equation whose two roots are distinct. y=C1em1x+C2em2x

Q: x°dy + xydx = x²dy + 2ydx; y = e when x = 2

A: Given: To Find: To solve the given differential equation.

Q: (ry +y ) y' = y?. y' = エーリ+3 y' =

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Q: Find the solution to the differential equation y'-2ty = 4t

A: Solve the above differential equations.

Q: Solve the following first order linear differential equations.   y' - 2y = 1 - 2x

A: For linear differential equation,dydx+p(x)y = Q(x)Solution is :y x I = ∫IQ(x) +Cwhere I = e∫p(x)dx

Q: 15.) y = ae* + blnx + cx + d

A: We have to find the differential equation of the equation y=aex+blnx+cx+d, which is a general…

Q: (x*y- xy")(xdy + ydx) + dy = 2xdx

A: To solve the differential equation we use some special form

Q: 6) y' = 2x-3y+4 x+y+2

A: Differential equation

Q: Find the general solution of the differential equation.For x=3,m=11

A: Introduction: A higher order linear homogeneous differential equation has only complementary…

Q: y = cqe¯* + C2e4* – C3e* + cze2x

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Q: Find the differential equation whose solutions correspond to the following equation a. cx2 + x + y2…

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Q: Q1. Solve the differential equation to find y: (1+x) +y = v

A: Note: We will answer the first question only as the exact one is not specified. Please resubmit the…

Q: =*y' + xy + 2 = 0. 2xy' 2.

A: Since we are given with the multiple number of question and our guideline is solve first question…

Q: A/ find solution for the differential equation below: Y"' - 6Y" + 11Y – 6 = 0

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Q: Find the differential equation whose solutions correspond to the following eq 1. y = Ce¬* + Cze²x 2.…

A: We need to find the differential equation with the help of given equations. This can be evaluated as…

Q: dx + 2xydy: こD (6x²+y²)

A: follow the procedure given below.

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.