8. The solution of the differential equation (x*+1) +(x°* +1) = 0 de 1-x y=: 1+x a. Ob. y=2+x 1+x y=- 1-x Oc. od. y=x(x-1)

Q: 8. The differential equation (2x-xy-2y+3}dx-(x*y+2xkty = 0 is exact because ÔM ON

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Q: 2. Show that k(x, y) = e2ª cos (x + In y) is a solution to the differential equation 2k – ykya = 5k.

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Q: Find the general solution of the first-order linear differential equation for x > 0. (Use C for any…

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Q: 8. Use a substitution to solve the homogeneous 1st order differential equation (x – y)dx + x dy = 0

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Q: What is the particular solution to the differential equation = (x – 1)(1 y) with the initial…

A: givendydx=(x-1)(1-y)we will solve this equation by Variable separable method

Q: The Bernoulli's form of the differential equation 2x³dy-− y(y² + 3x² ]dx = 0 is

A: As per our norms we have to write one question at a time kindly repost remaining questions.

Q: For the second-order differential equation y" + 9y = 6 cos x: a. Show that y = cos x is a solution.…

A: The given differential equation is: y''+9y=6 cos x

Q: 5 Find the general solution of the differential equation: (1+x³ ) dy – x² y dx = 0 %3D Then find the…

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Q: Determine the values of r for which the differential equation y + 2y = 0 has solutions of the form y…

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Q: 6. Solve for the general solution of the differential equation using exact equation [2x + y cos…

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Q: 10. Find the general solution to a sixth-order linear homogeneous differential equation for y(x)…

A: We first write the possible roots of the auxiliary roots  of auxiliary equation of  the sixth order…

Q: # 2.) Given the differential equation, y'=4cosx-3y, y(0)=1, a.) Use Euler's Improved Method to…

A: Given the differential equation, y'=4cosx-3y With the initial condition y(0)=1 Here,…

Q: 3. The Bernoulli's form of the differential equation x' ydx+(3x-y'dy=0 is

A:

Q: 1. A solution for the differential equation is y = e"x A, sin (vx) + A, cos (vx), where m and n are…

A: Let's find.

Q: 2) Show that y = A cos x + Bsin x, where A and B are constants, is a general solution of the…

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Q: (4x3 – 3y²)dx + 6xydy = 0 Ans: 2x3 + 3y² = 2x %3D

A: first will convert the given differential equation into linear differential equation of first order…

Q: 1. The standard form of the general first order linear differential equation in y is 2. The linear…

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Q: [6] Find the solution of the first order ordinary differential equation (1– 3y2) dy – x sinx dx=0, y…

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Q: Find the general solution of the first-order differential equation                     (x + y) dx −…

A: To Determine: Find the general solution of the first-order differential equation by any appropriate…

Q: Find the particular solution of the differential equation with the initial condition given below.…

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Q: 1. Find the general solution of the linear differential equation using undetermined coefficients,…

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Q: Find the general solution of the first-order linear differential equation. e2x y' = 4 – e*y (Express…

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Q: 1 xdy – y(1+ y cos 2x)dx = 0 ;y(0): Ans: 2x + y sin 2x = 0 2

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Q: 1. A solution for the differential equation is y = e"* A, sin (vx) + A2 cos (vx) , where m and n are…

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Q: 16. What is the particular solution of the linear differential equation y' +y = sec e", whose…

A: The solution is given as

Q: 3. The Bernoulli's form of the differential equation x' ydx+(3x - y³ dy=0 is

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Q: We consider the following differential equations: xy" + xy' - (x − 3) y = 1 pour x > 0. Give the…

A: Consider the following differential equations: xy''+xy'-(x-3)y=1 for x>0   To Find: General form…

Q: x2+1 y'= Ans: y = + x + In(x – 1)² +c = -X - X-1

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Q: x+ y, (e* + In y)dx + (dy = 0

A: We have to solve the given first-order differential equation…

Q: 7. Choose the appropriate table for the differential equation X y ଶ୪ X y dx X Y -201 -4 1 2 2 -1 -1…

A: The solution is given below

Q: 3 2 2. x" - y' + 4x y = 0, x > 0; y,(x) = sin x

A: Given:          xy''-y'+4x3y=0 , x>0 y1(x)=sinx2    Use reduction of order method   let…

Q: d³y +3(1- a)z² d´y dy + (3a? – 3a +1)z- - a'y = 0 dz dz

A: We have to find the value of the variable a.

Q: 4. Solve for the general solution of the differential equation using homogenous equation. [x cos?…

A: A homogeneous differential equation is an equation containing a differentiation and a function, with…

Q: Q3. Second order non-homogeneous ordinary differential equation is given as: y"+ y' – 2y = x² - x+e*

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Q: 1. Find a homogeneous linear differential equation with constant coefficients whose general solution…

A: y=c1cosx+c2sinx+c3cos2x+c4sin2x For c1 and c2 α=0, β=1 α±βi0±1i0±i m-im+i=0m2+i2=0m2-1=0

Q: x(1+ y³)dy + ydx = 0 ;y(1) = 1 Ans: In(xy)3 + y3 = 1

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Q: Solve the differential equation with the given initial condition. dx 1 x with x(2) = 7 3 y E - - dy…

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Q: Find the general solution of the non-homogeneous differential equation Y” –  2Y’  + Y  =  4 cos x

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Q: 2) find the complete solution of the differential equation x dy +Jx²-y*dx = ydt

A: given xdy+x2-y2dx=ydxxdy=(y-x2-y2)dxdydx=(y-x2-y2x)put…

Q: 4. Find the general solution of the differential equation using the method of undetermined…

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Q: find the solution of the differential equation     dy / dx = y / (y-x)  with y(5) = 2

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Q: Find the solution to the initial-value problem. y' = −8x tan(y), y(0) =  ? 2 y =

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Q: 2) Show that y = A cos x + Bsin x, where A and B are constants, is a general solution of the…

A: Solved below

Q: 4. Find the general solution to the differential equation y" + 4y = cos 2x (where y' = ) dx

A: The general solution of a higher-order linear non-homogeneous differential equation is the sum of…

Q: 2) Show that y = A cos x + Bsin x, where A and B are constants, is a general solution of the…

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Q: (b) Without solving. What is the form of a particular solution of the given differential equation y"…

A: To find  The form of a particular solution of the given differential equation

Q: 1. Find the general solution of the differential equation 1 sin z y*y' + =y°

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Q: 2. Find all values of r for which y = e™ is a solution of the second order differential equation y"…

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Q: 45. The particular solution of the differential equation x^2 dx - (y+1) dy = 0 if at x=1, y3D0 is_

A: Given differential equation is x²dx - (y+1)dy = 0

Q: 5. The Bernoulli's form of the differential equation xdy-[y + xy ³ (1 + ln x)]dx = 0 is In

A: Given xdy-y+xy3(1+lnx)dx=0