1. FIND THE GENERAL SOLUTION OF THE FOLLOWING DIFFERENTIAL EQUATIONS: dy 1. dx dy = xy + 3x-3x' dx

Q: (15) Investigate the stability of the stationary solutions of the following differential equation:…

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Q: dy + у 1-y %3D ху dx

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

Q: 4. Find the general solution of the differential equation: dy dy + 14y = x? dx %3D dx?

A: d2ydx2-9dydx+14y = x2 Auxillary equation is m2-9m + 14 = 0 m2-2m-7m+14=0 m(m-2)-7(m-2)=0 m=7,2

Q: 1- Find the solution of the following second order differential equation d²y(x)dy +x +x² y(x) = 0…

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Q: dy 1- the general solution of the differential equation 2ху is 1+x2 y =........ dx

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Q: 2. Find the general solution of the differential equation: dy dy -5 + 6y = e* dx? dx

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Q: 2. Find the general solution of the differential equation: dy ip 5 + 6y = e ,3x - dx? d.x

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

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Q: 5. Find the solution of the differential equation that satisfies the given initial condition. dy =y²…

A: Topic- differential equations

Q: Find the general solution of the given second-order differential equation. Зу" + 2y' + у %3D 0 y(x)…

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Q: Find the general solution of the given differential equation. d'y 4 dx dy dy 5- = 0 - dx dx

A: Given differential equation is d3ydx3−4d2ydx2−5dydx=0 We have to find the general solution of the…

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

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Q: Find the general solution for differential equation.

A: To find the general solution: dydx+4xy=4x Solution: dydx+4xy=4x On simplifying further we get:…

Q: Find the general solution of the given second-order differential equation. y" + 16y = 0 %3D y(x) =

A: We have to find

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: dy 2 dx y+2 x+y- 1

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Q: 5. In the differential equation (xy +1)dr+x(x+4y-2)dy = 0, the integrating factor is

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Q: Find the general solution of the first-order linear differential equation (dy/dx)+(1/x)y = 6x + 2…

A: Given- dydx+1xy=6x+2 To find- the general solution of the above first order differential equation.…

Q: determine the value of C of the general solution of the separable differential equation dy/dx= xy^2…

A: From the given problem: dydx=xy2 So, dydx=xy2dy=xy2dxdyy2=xdx Now integrate on both side:…

Q: (군2-1) 을 + 2y3 (+ 1)°

A: Given ODE : (x2-1)dydx+2y=(x+1)2 ⇒dydx+2yx2-1=(x+1)2x2-1⇒dydx+2yx2-1=x+1x-1 Which Linear…

Q: Find the general solution of the given differential equation. (x + 1) dy + (x + 2)y = 2xe-x dx 11

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Q: Solve the non-homogenous differential equation below dy 2y + x - 3 dx y + 2x – 3

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Q: Obtain the general solution of this differential equation: xydx - (x+2) dy = 0

A: Given : The differential equation xy dx - (x + 2) dy = 0.   To obtain the general solution of the…

Q: Find the general solution of the given higher-order differential equation. dy 16. dx4 + 40 + 25y = 0…

A: We will find out the required general solution.

Q: Find the particular solution of the given differential equations. 3. (xy + x)dx = (x²y² + x² + y² +…

A: Find the particular solution of the given differential equations.3. (xy + x)dx = (x²y² + x² + y² +…

Q: Find the particular solution of the following differential equations with the given condition. 3) dy…

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Q: In the differential equation (6x - 3y + 2)dx-(2x - y - 1)dy = 0 , we let the substitution dx =…

A: Please see the answer below.

Q: Find the indicated particular solution of the given differential equation. dy 3 - 2x; y = 7 when x =…

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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: dy y/x + x²/y²; y(1)=0 dx

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Q: Find the General Solution of this Differential Equation 1. (xy² + x) dx + yx² dy = 0

A: See detailed solution below. Using properties of derivative and variable seperable method

Q: 1. Find the general solution of the differential equation: dy, dy + dx3 dºy dy = 0 dx6 dr5 dx?

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Q: 5. In the differential equation (xy +1)kdx+ x(x+4y– 2)dy =0, the integrating factor is

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Q: Find the solution of the following second order differential equation d²y(x) dy +x- +x² y(x) = 0 dx…

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Q: Find the indicated particular solution of the differential equation. dy dx + 7y= -2e - ⁹x; x = 0…

A: Topic = Differential equation

Q: 2. Find the general solution of the differential equation: dy dy 5 + 6y = e3x dx - dx?

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Q: (x + 2y – 1)dx + (3x + 6y)dy = 0.

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Q: In the differential equation 4(3x+ y– 2)dx– (3x+ y)dy = 0, we let the substitution dw=

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Q: 2. Find the general solution of the differential equation: dy 52 + 6y = e2r dx? dx

A: Solution is given below:

Q: 3. In the differential equation (2x+ y)dr-3(2x+ y+4)dy = 0, we let the substitution dy =

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Q: Determine the general solution of the given Differential Equation 3x (xy – 2)dx + (x³ + 2y)dy = 0

A: Proceed as shown below...

Q: 3 Find the particular solution of the differential equation dy (x+2)= y+2 dx y(0) = 1

A: To Determine :-  The particular solution of the differential equation x+2 dydx = y + 2            y0…

Q: I. FIND THE GENERAL SOLUTION OF THE FOLLOWING DIFFERENTIAL EQUATIONS: dy 1. dx dy = xy + 3x - 3x dx

A: As per our guidelines we are allowed to do 1 question at a time.  Please post other questions next…

Q: Find the general solution of the given differential equation: dy = x²y %3D dx

A: Solving

Q: Find a set of solutions to the following differential equations 1. (x2+ 6y2) dx - 4xy dy = 0 ; when…

A: We have to find

Q: Find the general solution of the given higher-order differential equation. у" + 3y" + 3y' + y = 0…

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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: x²dx + y(1 – x)dy = 0

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