Obtain the general solution of the following equations:   (x-4y-9)dx-(4x+y-2)dy=0

Q: Determine whether the equation (3x + 2y)dx + (2x + y)dy = 0 is exact. Find the solution if it is…

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Q: Find the solution fo (x^3-y^3)dx + xy^2

A: Here we have,  (x3-y3)dx+xy2dy=0⇒(x3-y3)dx=xy2dy⇒dydx=(x3-y3)xy2 ..............(1) Which is a…

Q: Find the general solution for the equation: dy=(x^2+x)y^3dx

A: Given:          dy=x2+xy3dx

Q: Obtain the general solution to the equation. y(dx/dy)+6x=3y^4

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Q: Write the linear equation in proper form and solve the initial value problem. dy – 2y – 1, y(1) = 3…

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Q: find the general solution of the given equation. 4 d2y/dx2 - 12 dy/dx + 9y = 0

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Q: Find the solution of (x-2)dy = (3x² - 6x - y)dx given y(0) = 4.

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Q: a) Find the general solution of the given equations of the line (2x - 5y + 10)dx+ (7x + 3y - 8) = 0

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Q: Find the general solution of dy -2x6 dx y-4

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Q: (x + y – 2) dx + (x – y + 4) dy = 0 |

A: Given:-(x + y - 2) dx + (x - y + 4) dy = 0To find: Find the family of equations

Q: Find the general solution for the equation dy/dx=(2x/y)e^y+2x

A: Given the differential equation, dydx=2xyey+2x    ⋯⋯(1) Rewriting equation (1),…

Q: Solve the Cauchy euler equation d³y x3 dx3 3x2 d?y dx2 2 + 6x -6y = 3 + Inx³ dy dx

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Q: Solve the equation dy, 3y + dx +2 = 3x, y(1) = 1.

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Q: The general solution of (2x2 + y) dx + (x²y – x) dy = 0 is 4x2 + Dy² -Dy D

A: Given that 2x2+ydx+x2y-xdy=0Solution…

Q: Find the general solution of the given equation y" + y = 0

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Q: Use any appropriate method to find the general solution of each of the following equations. dy - y²…

A: Given differential equation is, x2dydx-y2=yx+x2

Q: Find the general solution of = 8e-4x %3D dx

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Q: Obtain the general solution of the following equations:    2y(x2-y+x)dx-(x2-2y)dy=0

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Q: Determine the solution of the equation using coefficient s linear in two variables metho: (x − 3y +…

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Q: The equation (x - 3y)dy = (2y + 4)dx is exact.

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Q: B) Solve the equation (x+y-1)³ dx+4(x-2) dy=0.

A: Solution

Q: Find the equation of the solution to dy/dx=x4y through the point (x,y)=(1,5).

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Q: Solve the first order equation (3r²y + 2ry)dz + (z³ + x² + 2y)dy = 0.

A: In the given question, the concept of the differential equation is applied. Differential Equation A…

Q: Find the general solution of the followin d² y equation 5 + 4y = 8 +5. dx2 dx

A: General solution is sum of particular integral and complimentary function.

Q: Obtain the general solution to the equation. dx y dy + 6x=5y

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Q: Consider the problem y' =1-2.xy, y(0) = 0 . %3D Find the solution of this D.E.

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

Q: Find the general solution of the equation, d²y dy 4 + Зу %3D0 dx dx?

A: Since you have posted a multiple question according to guildlines I will solve first question for…

Q: Solve and find the domain in which the solution is defined. dy/dx = (y2-xy-x2)/x2 , y(-3)=-6

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Q: Choose a non-exact equation and solve. (xy- 2y²)dx - (x² – 3xy)dy=D0 1.

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Q: Find the general solution of the lines Зу + 2 y - 2 )dx + ( 2x -+ 1 )dy = 0 4 2

A: Let us consider the given differential equation f(x,y)dx+g(x,y)dy=0 Using substitution,  x=X+hy=Y+k…

Q: Find the solution of the following equations using method of substitutions. A. (2x-2y+1)dx +…

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Q: d³ y dx³ 2d²y dx² 1 3dy=0 dx

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Q: Obtain the general solution of the following equations:   1.) y(y3-x)dx+x(y3+x)dy=0

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Q: determine the general solution of the equation. x(y'-x)dx-y(y'+x)dy=0

A: we will integrate this equation and find the solution of the equation

Q: Obtain the general solution to the equation. (x² +19) dy dx + xy - 2x = 0 The general solution is…

A: Using integrating factor method

Q: dy 2y+3\2 dx 4x+5. ||

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Q: Solve the Solution (6x+y^2)dx+y(2x-3y)dy=0.

A: Given differential equation is in the form Mdx+Ndy=0 Where, M=6x+y2 and N=2xy-3y2 If ∂M∂y=∂N∂x then…

Q: Solve the particular solution of the equation dy/dx = 3x² - 2x, when y=2 and x=-1.

A: We can solve the given problem as follows:

Q: Solve for the particular solution: dy + 를y3D -2°y"; y(-1) %3D2 dz

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Q: Solve the equation. (4x2 + 2x-1y)dx + (x²y° - 1)dy = 0

A: Given: Given differential equation is 4x2+2x-1ydx+x2y3-1dy=0 we want to solve this ODE

Q: Find the general solution. dy - 2y +4x3 dx

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Q: Find the general solution of (2x – y) dy = 2y – x - da

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Q: Solve the DE: 2 dy 3 dx 3x² + y² xy

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Q: Find the solution of y (4x + y) dx – 2 (x² – y) dy = 0

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Q: Q1. Find a general solution of the following equation: 2x(dx + dy) + y(dy – 5dx) = 0

A: Here we have,  2x(dx+dy)+y(dy-5dx)=0

Q: Solve the following equations: a) d²y dy dx² - 3 = 9, when x = 0, y = 0, dx dy 3 b) 2 d²y - dx² dx -…

A: Use the given differential equations.

Q: Find the complete solution of d2y/dx2 +2dy/dx+y =sinxcos2x.

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Q: Obtain the general solution to the equation. dy y + 7x +1

A: Here we have to find general solution of differential equation

Q: Solve the following equations: y dy x² + y²-1 x dx 2(x²+y²)+1 + 0

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Q: Solve the (1+) d x = (b an y -x) dy

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