4. Solve the differential equation (1+ y² + xy²)dx+(x°y+ y+2xy)dy =0.

Q: Solve the linear differential equation dy 2y x2 %3D - dx 1+x2

A: Given differential equation is dydx - 2yx = x21+x2

Q: Q2-Solve the differential equation dy = - y xcos² (-) dx

A: I am attaching image so that you understand each and every step.

Q: solve the differential equation of (x^3 +xy^2-2a^2)dx+(x^2y-y^3-yb^2)dy=0

A: For differential equation ,M dx+N dy=0 is tobe exact if∂M∂y=∂N∂xthen solution is∫M dx+∫ N…

Q: 1. Solve the differential equation: (x – 2y) dx + (2x + y) dy = 0

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Q: (6) Solve the homogeneous differential equation (x – y)dx – 2xy’dy = 0 - |

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Q: 5. Find the solution of the differential equation y =- xy + xy³ (Bernoulli)

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Q: Solve the differential equation: [y³ – y²e* – cos(x – y)]dx + [3xy² – 2ye* + cos(x – y)]dy = 0 ;…

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Q: _6// Solve the differential equation 2y³dx – (yx? + y³)dy = 0

A:

Q: 1. Find the general solution of the differential equation: d°y d'y dy , dy - - dx6 dæ3 dx2

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Q: 2. Solve the differential equation (x* - 2xy² + y² )dx − (2yx² − 4xy³ + sin y)dy = (

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Q: 2. Find the general solution of the differential equation y'+2xy 2xe-x2

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Q: (4) Find the general solution of the differential equation (D² + 2D+5)y= sin hæ

A:

Q: 3. 3x²y dx - (x³ + y³)dy = 0, y(1) = -2

A: Solution to the differential equation

Q: 3. Get the general solution of the differential equation (x+2y-4)dx- (2x+y-5)dy%3D0.

A:

Q: 1) Solve the differential equation x² + y² ) dx - :- (ryVx² + y²) dy = 0.

A: the given differential equation is: x3+y2x2+y2 dx-xyx2+y2 dy=0 we have to solve the given…

Q: 4) (y + x² ) dx = xdy Find the general solution to differential equations

A: We have given a differential equation   y + x2 dx =  x dy ydx + x2 dx = x dy x dy - y dx = x2 dx

Q: Solve the differential equation. (y+2y+2e*y* )dx-2(x+1)qy =0

A: Consider the provided D.E,

Q: 1. Find the general solution of the differential equation cos x 1. dy 2 y2-4 dx 2y

A: Solve differential equation by seperation of variable:-

Q: 1. Choose a solution to the differential equation y" - y = x²e² + 5.

A:

Q: 4. Solve the homogeneous differential equation x'dy+(y² +xykdx = 0.

A: To solve the given homogeneous differential equation.

Q: 2. Solve the Differential Equations. (y² - xy )dx + x² dy HO

A: To solve the given differential equation.

Q: 1 Solve the differential equation: dy +(4x-7) y= 2x° dx

A:

Q: 5. Find the solution of the differential equation 2dy + ydx = y'(x-1)dx (Bernoulli)

A: given that

Q: Find general solutions of the differential equation      3y^2y'+y^3=e^(-x)

A: Consider the provided differential equation,

Q: y+2y)dx+(xy²+8j"-4x)dy=0

A:

Q: 5. Find a general solution of the differential equation: y" + 4y' = 2x – 1

A:

Q: (5) Find the general solution for the exact differential equation (x² – 4xy – 2y2)dx + (y? – axy –…

A: The given differential equation is x2-4xy-2y2dx+y2-axy-2x2dy =0

Q: b. Solve the exact differential equation (9x* +5x*y*)dx +(4x°y° -7y° )dy = 0.

A:

Q: Solve the differential equation dy y(0) = -1. dx 3+1 There is no need to isolate y.

A:

Q: (5) Find the general solution for the differential equation (x² – 2xy – y²)dx – (x + y)²dy = 0.

A: It is a first order non linear ordinary differential equations and also it is a exact equation…

Q: 3. In the differential equation (y -x -4r-1dy + 2y(x+y+2)dx = 0, 心

A:

Q: (x - y) dx +(3x + y) dy = 0

A: The given differential equation is: (x-y)dx+(3x+y)dy=0...(1)

Q: 3. Solve the differential equation (xr² + y² )dx + xy dy =0.

A:

Q: I. Find the general solution of the given differential equation. 1. y' + 2xy = x3

A: As per the guidelines, we are supposed to answer only one question at once. Kindly repost the other…

Q: Solve the exact differential equation: (a?y3 - 1 dr+y?dy 0 1+ 9x2

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Q: Solve the linear differential equation of order one 2x(y−x^2)dx+dy=0

A:

Q: I. Solve the differential equation. (y-1ldv +x Cx+1)dy = o

A: Solution:

Q: x*y" - 2xy' +2y = In x |

A:

Q: Q1) Solve a first order differential equation. dy -x + Vx² + y² dx y

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Q: Solve the differential equation. 14. ( 1 – xy)^-2 dx + [y^2 + x^2 (1 – xy)^-2] dy = 0

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Q: 5 Find the general solution to the differential equation y - where x > 0. y = +C

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Q: 3.(i) Solve the Non-linear differential dy equation dx y = 4 • XVG 1- x2

A: Consider the provided question,

Q: The solution of the differential equation (x³ + 3xy²)dx+ (y³ + 3x?y)dy= 0 is

A:

Q: 4. In the differential equation (y -x -4x-1)dy + 2y(x+ y+2)dx = 0, MN

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Q: 3. Find the general solution of the differential equation y" + 4y = 2 + e²" cos 2x

A: Given differential equation is 2nd order differential equation. General solution= Complementary…

Q: 1. Solve the differential equation (x² + y)dx + (x + y²)dy = 0.

A:

Q: 2. (x+2y-1)dx - (2x + y - 5)dy = 0

A:

Q: Consider the differential equation: 1 y"- 3y' + 2y = 1+e* What is the general solution?

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Q: y' - 5y = -xy, y(2) = 1

A: