Example 2: Find the particular solution of (x – y)dx + (3x+y)dy = 0 when x = 2 & y = -1.

Q: (x² + y²)dx – xydy = 0 -

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Q: 1. Determine the general solution of (x + 3y)dx - x dy = 0

A: Here in 1. we have to find general solution of given differential equation,        As per our…

Q: 6. Find the general solution of the system: :) X+(- sint X = -2 cos t

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Q: 4. General solutions of differential equations (x² + y² +x)dx + xy dy = 0 is..

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Q: The general solution of the differential equation d²y dy X- dx .2 +y3D2lnx dx

A: Given differential equation x2d2ydx2−xdydx+y=2lnx.......1. We have to find the solution of the…

Q: The general solution of the differential equation x²y" - 2y = Inx %3D is

A: Cauchy Euler differential equation of second order: x2y''+xy'+y=0 Let us consider x=ez Replace:…

Q: Problem 2.3 i. and 2.3 ii

A: Given initial problems are

Q: (a) Find the general solution of the partial differential equation: (y² + u² – x²)p – 2xyq = –2xu |…

A: Lagrange's form Pp+Qq=R ⇒dxP=dyQ=dzR and the general solution is given by f(c1,c2)=0

Q: Find an explicit solution of the given initial-value problem. x2dy 3D у - ху, у(-1)%3D -4 dx

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Q: b) Use the initial condition x(0) = 2 to find the particular solution of dx - 2x = 2e3t dt

A: We have to solve the given initial value problem  As per the answering guidelines we need to answer…

Q: Part II Solve the initial value problem. (y°cosr– 3x?y– 2x) dx+ ( 2ysinx – x³ + Iny) dy = y (0) = e…

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Q: (2) The particular solution y,(x) to the differential equation y" + 100y = sec2 (10x) is of the %3D…

A: Given y"+100y=Sec2(10x) ---1Compairing with y"+q(x)y'+r(x)y=g(x).Auxilliary equation corresponding…

Q: The differential equation 20x+x²y=2x+3₁ (0)=5 is dx O linear with fixed constants O undeterminable…

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Q: Find an explicit solution of the given initial-value problem. dyy²-1 = y(7) = 7 dx x² y =

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Q: The solution of the differential equation dy dx 6. is 6x + C 6lnx + C | 4 6x + C 5 6lnx + C 2

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Q: Find an explicit solution of the given initial-value problem. x20Y = y - xy, y(-1) = -2 dx y =

A: Given initial value problem, x2dydx=y-xy,y-1=-2 Find the explicit solution of this problem.

Q: 1. Find the general solution of dy dx + y = x

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Q: An integrating factor for the linear differential equation Y'- 2y = 4x is H= O A. - 2x O B. 2xe2x…

A: Given differential equation is y'-2y=4x This is linear differential equation.

Q: Consider the following nonlinear equations. fi = sin(6x,)+cos(4x,)–1.5x, =0 f2 = e* +6x, +4x, = 0 f3…

A: To solve a system of three nonlinear equations with three unknowns, use the modified Newton Raphson…

Q: 3. Solve the Bernoulli DE: 5 dy - 5y : dx | - 2

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Q: 2. Give the general solution of xy'dy = (x³ +y³)dx in explicit form.

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Q: 4. Solve the initial value problem- dx dy 3x? +4x + 2 2(у-1) y(0) = 2 and state the interval in…

A: Given differential equation is : dydx=3x2+4x+22y-1 To solve the given differential equation.

Q: Solve the differential equation (1 − xy)−²dx + [y² + x²(1 — xy)−²] dy + x²(1 − xy)−²] dy = 0; y (2)…

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Q: 1. Find the general solution of dy dx +y=x

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Q: Solve the separable differential equation 7e-3x+2x -xcosx y' = -6y3

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Q: - Find the solution of the partial differential equation Z, = 6x + y

A: Given : Zxy  = 6x2 + y    Now we Find the solution of the partial differential equation .

Q: 9. [ 2x + y cos (xy)] dx + x cos (xy) dy = 0

A:

Q: 9. Find the particular solution for each initial value problem. a) (2x + 3)y = where y(0) = 1 dx b)…

A: Particular solution:         The solution obtained by giving particular values to independent…

Q: Find an explicit solution of the given initial-value problem. () - 1 dx 3(x2 + 1), dt X =

A: Given query is to find the solution of the differential equation.

Q: Find general solutions of bernoulli differential equations.   (1 - x^2) y' - xy = axy^2

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Q: Find an explicit solution of the given initial-value problem. x2 dy = y - %3D у — ху, у(-1) %3D -1…

A: Firstly we will solve the given differential equation by using variable separable form then…

Q: Example 5: dy Find the particular solution of, y(1+x²)÷= 2x(1 – у?); y(0) = 0 dx

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Q: Find the general solution of DE:  1. (x-4y-3)dx - (x-6y-5) dy = 0

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Q: Find an explicit solution of the given initial-value problem. √2 √₁-y² dx - 1- √1-x² dy = 0, y(0) =…

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Q: 4. (a) dzy Solve: dx2 + ( = 0. (b) Solve xy" + (1 – x)y' – 2(1+x)y = e-*(1 – 6x) by the method based…

A: We have, d2ydx2+dydx+dydx3=0 ..i Put dydx=v ⇒d2ydx2=dvdx Now substitute in equation i we get…

Q: -dt solves the initial value problem 35. Show that y = x² + d² y 2 x²* 3; y'(1) = 3, y(1) = 1. dx…

A: Given

Q: -2 2 dx dt -12 8 with the initial value -2 x(0) = -5 x(t) =

A:

Q: Example Find the solution of the differential equation x'+y² 2ху dy dx that satisfies the condition…

A: given,

Q: Find an explicit solution of the given initial-value problem. 1 √1-y² dx √1-x² dy = 0, y(0) = = y =

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Q: Find an explicit solution of the given initial-value problem. dx = = 6(x² +1), x(1) = = 1 dt x = tan…

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Q: 3. Solve the initial value problem of y(-1) = 0 dx x+3

A: Since the student has posted multiple questions and does not mention any specific question, so we…

Q: 3 9 dx dt -1 -3 with x(0) 4 Give your solution in real form. X1 = X2 = ||

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Q: Find an explicit solution of the given initial-value problem. √1-y² dx - √1-x² dy = 0, y(0) = 113 2…

A: Here in this question, we have to find out the solution to the given differential equation.

Q: 3. Solve the initial Value Problem x dy +(y-cos x)dx = 0, y )=0 %3D

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Q: Example :- Solve the following differential equation where d²y + y = 0 dx2 Subject to boundary…

A: As per the question we are given a second order linear homogeneous differential equation with…

Q: Solve (5x2y2 O a. b. 2 ln 3 In a In xy² + 17y²) dx (x+2)³(x²+9) y³ |(x+2)³(x²+9) Y - -1 3 tan-¹() =…

A: Given 5x2y2-xy2+17y2dx-x3y+2x2y+9xy+18ydy=0

Q: 2. Give the general solution of xy dy = (x³ + y³)dx in explicit form.

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Q: Find an explicit solution of the given initial-value problem. √₁ - y² dx - √1 - x² dy = 0, y(0) =…

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