Find the general Solution of the diff. equ- x*y" +zxy-2y=D0 ?

Q: Find the solution of the following IVP: y(t) = dy -2ty=9t²e², y(0) = 5. dt

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Q: xarctanydx + dy = 0 2(1+ y²)

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Q: Find the general solution to the given DE x²y" – 3xy' + 4y =x?Inx, x>0.

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Q: (x² + 4xy + 2y²)dy + xydx = 0

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Q: d²y - y = у 3 10sin?x %3| dx2

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Q: (у — ӕ + хусotx)dx + zdy — 0 y(0)= 3

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Q: Find the general solution to the given Euler x?y" – 3xy' + 9y = 0

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

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Q: 'ind the Wronskian of any pair of solutions to 2t?y" + 3ty' – y = 0,t > 0.

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Q: What is the general solution of rydx (2² + 3y²) dy = 0 ? %3D 6y² In y = C O + 6y² In y = Cy² %3D

A: Given: xydx-(x2+3y2)dy=0

Q: D = {(r, y) : 1 <Ise, 0<yS In(r)}

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Q: dy Use separation of variables to find the general solution to dr + 4xy? = 0. %3D

A: We have to sine given differential equation using seperation of variables

Q: (c) xy' = y(3– x)

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Q: Find the general solution of the DE dyldx = (x - y) / (x + y). O y^2 - 2xy – x^2 = C O y^2 + 2xy –…

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

Q: What is the general solution of (2xy + y) dr + (r? - r) dy = 0? %3D C(z 1) * y = Cr(z - 1) * O y =…

A: Given differential equation is variable separable differential equation of first order. We will…

Q: Let y(x) be the solution for the DE : y = (x + y – 1)2 If y(0) = 1, thenfind y(4)

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Q: d³y d²y, dy 4- + + 26 = x3 – 3 dx3 dx² dx

A: given differential equation isd3ydx3-4d2ydx2+dydx+26=x3-3for complemantry solution of given…

Q: Find he value of ds/du at u = 2 if s t2 + 5t and t (u? + 2u)/s %3D

A: Here, s=t2+5t and t=u2+2u13 So, s is a function t and t is a function of u. At u=2, t=(4+4)13=813=2

Q: Let y(x) = c1 + c2x + C3 et is a general solution for D. y" + ay' + by +cy 0, Find the value of a?

A: To answer the given question, we form a differential equation from given general solution.

Q: Determine the solution for this DE 2xy dx - (3xy +2y^2)dy = 0

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Q: Find the particular solution determined by the given condition. 3) y' = 7 ; y = 20 when x = 1 A) y =…

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Q: Find the complete solution of the DE (D3+6D2+11D+6)y=ex +cosx.

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Q: Let a ∈ R and find the solution to y'(t) - a y(t) = 0.

A: The given differential equation is dydt-ay=0 , a∈R.we will slove this by the method of  separartion…

Q: Find the solution of y" – by' + 9y = 16 et with y(0) = 2 and y' (0) = 1.

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Q: (b) Use the substitution u = x In y to solve the equation (ry + 2ry In² y + y In y)dx + (2x² In y +…

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Q: What is the specific value of x and y in the diophantine equation 17x + 23y = 157?

A: In this question we have to find value of x and y in Diophantine equation,

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

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Q: Suppose that the DE y"" (x) + 7y(x) =70 2³ +123 has a solution of the form y = Az³ + B Find the…

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Q: Find the complete solution of (x?y +y³ – y)dx + (x³ + xy² + x)dy = 0 Hint: Expand and Simplify

A: Hey, since there are multiple question posted, we will answer the first question. If you want any…

Q: Find the particular solutiona by inspection . Cpg4)y=と"43x Cp*+4>y = 8x +1 - 1se C 4D° + 4D+)y = te*…

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Q: Give the general solution to -y + 2 ху a) Os = + Cx² b) Oy =x+Cx? c) Oy = 7x o or - d) Oyl x² + Cx-…

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Q: Solve for the particular solution: dy = y + Vr2 – y?, y(2) = 0 %3D - da

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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: Find the general solution of the given second-order differenttial equation y" + 18y' + 81y =0 y(x) =…

A: we have to find the general solution of the given differential equation. y"+18y'+81y=0

Q: (8) 2xy = x2 + 2y² = x² dx

A: As per our guidelines we can answer only 1 question so kindly repost the remaining questions…

Q: Solve the diferential eguation with discasfssic Of soaL (4xy-y2) dx +(2x? - 2 xy + 2y?) dy=o

A: Given the differential equation is 4xy-y2dx+2x2-2xy+2y2dy=0 This is form exact differential equation…

Q: Determine a general solution for the DE : y" + 2k?y' + k*y = 0

A: We have to find the solution for given differential equation

Q: Find the solution of the given DE (y? – 2xy + 6x)dx – (x² – 2xy + 2)dy = 0

A: First we find out whether the given equation is exact or not then we solve.

Q: Find the complete solution of dy + ydæ = 2ry e" da 01= ye" (C- z) 01=yle(C-') O1= ye" (C + z*)…

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

Q: Given (x + 6y? ) dx - 4xdy = 0, when x = 1, y = 1. Find the particular solution.

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Q: Verify that y = c₁ex + c₂e4x is a solution to the DE: y" - 5y + 4y = 0.

A: We are authorized to answer one question at a time, so we are answering the first one, please repost…

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

A: Use the given differential and initial conditions.

Q: Find he value of ds/du at u = 2 if s t2 + 5t and t = (u? + 2u)

A: ds/du=9/2

Q: let y"(x) + y(x) = 0 be given What would be a suitable solution y(x)?

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Q: Find general solution of the DE 4x2y′′ + 8xy′ + y = 0

A: Consider the given equation. 4x2y''+8xy'+y=0 Let substitute the value is y=xm. Now, find the…

Q: 16z dV, where E is the upper hemisphere of x? + y² + 2² = 1

A: We have to find the value of the given triple integral ∫∫∫E16z dV where E is the upper hemisphere…

Q: 3. Find the genesral Solution: y* 5y^ +3y' -ay=

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Q: Find the solution of BVP 2. Uxy = 4xy+ex ; uy (0,y) = y, u(x,0) = 2

A: uxy=4xy+ex uy0 ,y =y u(x,0) = 2 To find solution of given differential equation

Q: Evaluate by using homogeneous D.E. 3 (3x? + y²) dx – 2xydy = 0 O ao3 = C(9x³ + y³) O ap3 = C(9x² +…

A: ANSWER: OPTION 2nd

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.