2) Find the general solution. y" + 3y" – 4y' – 12y = 0 d°x d*x d³x 12 ds d²x ds ds²

Q: (x² + y²)dx – xydy = 0 -

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

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Q: The particular solution of y(x+y)dx + (x +2y- 1)dy=0; y(0) = 2 by NEDE is

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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: Q6: Determine a particular solution of the equation d'y +4y 4x cos 2x dx Using D-operator method

A: The solution is given as

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: he Bernoulli equation for y by making 4y + y³. - following initial condition: u(0)

A: Introduction: A differential equation is a mathematical expression that contains the derivative of…

Q: 4. Solve the following equation by backward Euler's method and also trapezoidal method : y'(t)…

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Q: A particular solution of 4x² dy dx dy 4 is vx +8.x- +y = de

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

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Q: yy' – xcos(x²) = 0, y(0) = -2

A: We have to find the particular solution of the given initial value problem.

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: A: Compute dy at (2, 1) where y = xcos2x dx B: Solve for x: a2 (y³ + vx-4 +y sin2x) < 4cos2r Тдхду…

A: Please see the answer below.

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: Find a particular solution of the equation y2y' = cosx satisfying the initial condition y(0) = 0.…

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Q: 3. Show that the equation (6ry – y*)dx + (4y + 3x² – 3xy²)dy = 0 is exact. Hence solve the equation…

A: Solution:

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

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Q: 3. Obtain the Particular Solution when x = 4 and y = 1 (x+ y - 4)dx – (3x- y – 4)dy = 0

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

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Q: dy - y = xy2 dx

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Q: 7. Obtain the solution of (D² – 4)y = 16 + cos 2x using the method of undetermined coefficients %3D

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

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

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

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

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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: The solution of y" + y = 0 with initial conditions y (0) = 1 and %3D y = 2 is

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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: Solve for the general solution/particular solutio of the given using Bernoulli's Equation xydx + (x²…

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Q: b) Use the initial condition y(0)= 2.14 to find the particular solution of -2y+x² + 2x* = 0 %3D dx

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Q: Solve the general Solution of:  (xsiny/x- ycosy/xdx)dx + xcosy/x dy=0

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

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Q: Find the general solution of the Cauchy-Euler equation: x²y" – 3xy + y = x°, x>0.

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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: - Second order : non- homogeneous Equations with Constant Coefficients d²y 4-- + 16y = 10 cos 4x dx²

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Q: Exercise 7 Find the general solution 1. 6y'dx - x(2x + y)dy = 0

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

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Q: 7.Obtain the particular solution of (1 – xy)-2dx + [y? + x²(1 – xy)-²]dy = 0 when x = 2, y = 1

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Q: (1 – xy)-2 dx + [y² + x²(1 – xy)¯2] dy = 0; when x = 4, y = 1.

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

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Q: 4. Find the general solution of (x + y³) dx = 3xy² dy

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Q: The particular solution of y(x+ y)dx + (x+ 2y- 1)dy=0; y(0)= 2 by NEDE is

A: Let's find.

Q: 2. Obtain the general solution of: xy dx – (x² + 3y²) dy = 0

A: