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

Q: 2. Solve the general solution for the First Order Linear DE. удх %3D (еУ + 2ху — 2х)dy

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Q: Find the solution to the Bernoulli Equation. (3siny - 5x)dx + 2x²cotydy=D0 O x³(siny- x)2 = Csin?y O…

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Q: Solve the particular solution of the given DE: x(r^3-xy^2+2y^3 )dy-y(r^3+2y^3 )dx=D0 @r=1, y=1.

A: We have to solve given problem:

Q: Find the particular solutions of the following separable equations. 4 — 2х dy dx Зу? - 5' *+1 = 2y –…

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Q: Obtain the particular solution of the DE: 4(3x + y – 2) dx – (3x + y) dy = 0; when x = 1, y = 0…

A: Gg

Q: (1) 3 dy + y = dx 3 Find the general solution to: 1. -

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Q: dy =, with initial condition y(0) =2 is dx y The solution of %3D

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Q: Solve the homogeneous DE 3xy dx + (x^2 + y^2) dy = 0.

A: We will take the substitution y=vx, to convert it into separable variable form.

Q: dx ylnx dy || y + 1 X 2

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Q: Find the general solution of dy 2+ sin (x) dx 3(y – 1)² |

A: given,       dydx=2+sinx3y-12

Q: Find the particular solution of the initial value problem: dy 3x2(y? + 1), dx y(0) = 1 %3D

A: We can find the answer as below.

Q: 2. Obtain the particular solution A. yy' 2x(y+ 1) B. (x? + 1) dy = (y² + 1) dx

A: Topic :- Differential Equation

Q: I. FIND THE GENERAL SOLUTION OF THE FOI dy dy = xy + 3x - 3x dx 1. dx

A: As per our guidelines we are supposed to answer only one question

Q: 2. Obtain the general solution using Bernoulli's equation. Si l + x/ dx – 6x dy = 0

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Q: x'e* cos 3xdx + -dy = 0 Vỹ - 1 %3D

A: In this question, we solve the separable differential equation by direct integral. the differential…

Q: EXERCISE 1. dy ry+y Find the general solution of dr

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Q: Find the general solution of dy xy = 1+ y?

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Q: y_x + y х х — 1 dx

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Q: 6. General solution is y = x² In x + Ca² , EXERCISE 6. dy 2y = x? dx

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Q: we solve thd DE y dx 2x0y-0aer convedding it to oad sing an integrating tactor, then the solution…

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Q: dy 3. + Ay = w; y(0) = 0 and A> 0 dx

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Q: Solve the initial value problem. dy y = 7x e*, y(1) = 7 e - 7 %3D - dx The solution is y(x) =

A: NOTE: Refresh your page if you can't see any equations. . compare this DE with   so here we have

Q: Find the particular solution to DE:  ( xy^2 - x ) dx - ( 2x^2y - 3y ) dy = 0 ; y ( 1 ) = 2

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Q: 5. Find the particular solution (IVP) for the DE below: a) dx +2 =8x when x = 2, y = 6 b) 3y2 = 2x +…

A: Use variable separable method

Q: 2. Find the general solution of d²y dy +5- dr.² dx 6y=0

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Q: Q4: Find the general solution of d?y dy - 3 - 4y 3e2t + 2sin t - 8et cos 2t, dt dy y(0) = 2, (0) %3…

A: Given that  The differential equation  To find the general solution

Q: Find the solution of the initial value problem dy y , y(1) = 5 + tan %3D %3D dx

A: Given initial value problem is dydx=yx+tanyx   y1=π2

Q: Solve the homogeneous DE ( xy) dx - (x + 2y)^2 dy = 0

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Q: 4. Obtain the general solution of x? y dy dx

A: By Bartleby policy I have to solve only first one as these are all unrelated problems

Q: Question 1 Prove that 4 = ucy)e is a Solution for d24 - y°4 = 0 dy?

A: Given differential equation is d2ψdy2-y2ψ=0         (1) We have to check ψ=u(y)e-y22 is the solution…

Q: 2(y-4x2) dx + x dy

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Q: Solve the disfertial equation xy' -Y =Xtan ) %3D

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Q: Find the particular solution of dy - 2y = x³ sin 4x, y(1) = 2. dx %3D -

A: Using method of Linear Differential Equation.

Q: dy 2y = 2x/y %3D dx

A: The solution of the problem is given in the next steps.

Q: dy %3D 3 e*y* dx +

A: Givendydx+y3=exy4To Find:Solution of a given Bernoulli's equation

Q: Solve the Euler equation d²y dx dy -5y = 0 dx 31 d', 3x2 given that y(1) =1 and y'(1) = 2. intai

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Q: Solve the differential eavations ydx xdy = 0 x' +y° +y?

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Q: 2. Find the solution (implicit or explicit) dy (y+1) = 3sin(x). y(7)= 2 dx %3D

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Q: "ind general solution for dy dy + 3 + 2y = -20 sin 2t, y (0) = 2, y' (0) = 1. dt2 dt

A: Ode

Q: Find the solution to initial value problem d²y di? dy 14 + 49y = 0, y(0) = 1, y'(0) = 4 dt

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Q: Find the particular solution of (2x²y² + xy' )dx + 3 y? dy 0 that satisfies the condition y=1 when…

A: To solve the following differential equation

Q: olve the initial-value problem 2xy = In x, y(1) = 2 t? + 3u, t> 0, u(2) = y + x² sin x, y(7) = 0 dy

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Q: (у — сos-x)dx + cos x dy %3D 0

A: The given equation is y-cos2xdx+cosx dy=0 rewrite it as y-cos2x+cosx…

Q: Test for exactness and find the complete solution of dx + [ In 2(x-1) + dy = 0 х-1

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Q: 8) Find the general and particular solution for the following separable equation dy = -.5y, y(0) = 2…

A: The solution as follows :-

Q: Find the general solution of the given DE (x-3y-1)dx-(x-3y+5)dy%3D0.

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Q: d) Obtain the particular solution of (2x– 3y+4)dx +3(x-1)dy =0; when x=-1, y = 2

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Q: 3. Find the general solution of the Bernoulli's Equation. y = 5.4y – 12y, y(0) = 1. %3D

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