1. Use separation of variables to find the dy 2+ 4xy? = 0 general solution dx

Q: Find the general solution of d²y dy 4- + 4y = 0 - %3D dx?

A: The given differential equation is d2ydx2-4dydx+4y=0.

Q: Ex. Find the general solution to dy 1 -2.x dx X -

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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: 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 general solution to dy/dx= 6-x^2/2y^3

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Q: Reduce the given DE into Bernoulli's equation: - 2x*y¬ dx 3 y-4 dy_ y5 2x4 y4 dy dx dx 3 3 dy 2x* у…

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Q: Find the particular solution of dy/dx=6e^3x+1,andf(0)=0.

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Q: Find the general solution of

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Q: I. Find the general solution of the following: 1. dy - 2x²¹ dx y 2. dx = xy dx 3. dy = (6e³x + 1)dx…

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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: dx ylnx dy || y + 1 X 2

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Q: Solve for the general solution of (ylny-e^-(xy))dx+(1/y+xlny)dy=0

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Q: (1)Find the general solution for (- x) dx – (-y) dy = 0

A: Here, the given differential equation is  (2xy3-x)dx-(3x2y4-y)dy=0

Q: Obtain the General Solution of dx + xydy = y²dx + ydy.

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Q: Obtain the particular solution when x = 1 and y = 1 yl? - y² + 1) dn - xlx? - y? - 1) dy = dx – x(x²…

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Q: The solution to (2x – 4y – 3)dy = (x- 2y)dx is:

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Q: What is exact solution for dy/dx =(x2+y2)/(x+y)

A: Given: The given equation is dydx=(x2+y2)x+y

Q: The general solution of y2 + x2. dx e dy xy is = dx

A: Given: y2+x2dydx=xydydx ⇒dydx=y2xy-x2

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: If ey 9 dy 3x and y(1) = 2, then the particular solution y(x) is %3D dx

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Q: 1. Find the general solution: dy а) + 2xy = 0 dx dy b) (1+x) = 4y %3D dx

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Q: I. Find the general solution of the following: dy 2x 1.- dx y dy 2. xy dx 3. dy = (6e3x+ 1)dx

A: We have to find the general solution.     According to our guidelines we can do only one question so…

Q: Solve for the general solution of the given non-exact DE. (2y2 + 3xy – 2y +6x)dx + x(x + 2y – 1)dy =…

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Q: (1) Find the general solution for (+) dx + (--) dy = 0 %3D

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Q: Solve the bernoulli equation dx/dy+(2/x)y=-x^2y^2cos(x)

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Q: Find the general solution of  dy/dx + y/x= 3/y

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Q: dy dx ycos X こ y(o)=1 I +2y2

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Q: 9. Find the General and Particular solution of = 4y ; y= 3,when x dx

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Q: Find the general solution of the DE dy/dx = y(x – y) / x^2

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Q: dy dy = xy + 3x – 3x dx dx

A: The given differential equation is: dydx-x2dydx=xy+3x-3x3Therefore:dydx=xy+3x1-x21-x2

Q: Find the general solution of y'dx+(3xy+ y² –1)dy = 0

A: The differential equation is given as , y2dx+3xy+y2-1dy=0 find general solution.

Q: dy The solution of dx with initia y

A: Introduction: Separation of variables: This method is only practicable if the differential equation…

Q: What is the particular solution of (2x -3y) dx + (2y – 3x) dy = 0 when x 0 and y = 1 %3D O 22 + y?…

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Q: Find the general solution of dy/dx= e^3x+2y

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Q: In problems  determine by inspection at least two solutions of the   1. x dy/dx =2y,  y(0)=0

A: Given: xdydx=2y, y0=0 for solving given differential equation we will use variable separable method

Q: 4(3x+ y – 2)dx – (3x + y)dy = 0

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Q: 1. Find the general solution for d²y dy +10 +25y = 0. dx? dx

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Q: find the general solution of the given de dy/dx=2x+2xy^2/y+2x^2y

A: The given differential equation is dydx=2x+2xy2y+2x2y

Q: Obtain the general solution to the equation. dy 4. x+ 2y = x-3 dx

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Q: find general Solution of D.E. 4xydx +x'dy +3y^dx +2zydy=x

A: Note:- As per our guidelines, we'll answer the first  problem as exact one was not mentioned. Please…

Q: 1. Find the general solution of 3 + = y*(2x*) dx

A: Since you have posted multiple questions in this question which are not interlinked so I have solved…

Q: 4. Find the solution of dy 3y = x. dx

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Q: Find the complete solution First order DE dy = 2y3-ye dx Xe^y -6xy²-2y

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Q: 2Y – x²y² -2. dy dx

A: The given differential equation is: dydx=2yx-x2y2

Q: Find the general solution to the following DE. y +x² dy = 0 dx

A: Given DE, y2+x2dydx=0

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: The solution of (1 – y² )dx + (1 + x² )dy = 0 is: %3D

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Q: 1. Find the solution of dy xy %3D dx (1+x)(1+y)

A: The given problem is to solve the given ordinary differential equation. Given differential equation…