Example:- Solve the equation 1) (3y + e*)dx + (3x + cos(y))dy = 0 3) e* (ydx + dy) + e' (dx + xdy) = 0 dy 1+y²+3x²y dx 1-2xy-x³ = 2) 4) 2x ln(y) dx + dy = 0 (1+x²) y

Q: Solve x*y"- 2x(1+x)y'+2(1+x)y= x'

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Q: 2. Reduce to an exact equation and solve it: dy_2xsin 2 y+(2siny)/x² dx 2x²cosx-(2cosy)/x (2x²ysin…

A: GIVEN: dydx=2xsin2y+(2 siny)/x22x2cosx-(2cosy)/x             (2x2y siny -x y3sinx)dx +(x3siny +x3 y…

Q: 1 Evalute: dx (x'+2x+2)'

A: Please refer the attached image for complete solution.

Q: a) (3xy - y' + 2x) dx + (2xy 3xy + 1) dy = 0, y(- 2) = b) (ye* + 2e* + y²) dx + (e* + 2xy) dy = 0,…

A: A differential equation of the form M dx+N dy=0 is said to be an exact differential equation if it…

Q: y' + (=) y = xy²

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Q: solve A) y''-2y'=6e^2x-4sin(x)

A: Since you have posted multiple questions i can do first question as per our company guidelines…

Q: ( 3x²y + e' )dx + ( x³ + xe' - 2y)dy=0

A: We will first check whether given equation is exact or not ,then we find general solution…

Q: 1- x Vx2 + 9 dx. 1 2-5 dx 1+ sinx 3- sin'x cos'x dx

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Q: x* + 4 dx : %3D 3

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Q: Solve y(xy +2)dx +. x(2-2x²y²)dy = 0 .

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

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Q: (x^2-4x-4)(y^2+1)dx+2y(x^3-2x^2+4x-8)dy=0; when x=4,y=1

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Q: 7- I = [sec(2x) tan(2.x)dx cos(2x) 8- I = dx 4-sin (2x) csc (In(x)) 9. I: dx

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Q: (1+e' )dx +e" (1-)dy = 0 y

A: To find the solution of the below differential equation.

Q: (2xe + e*)dx + (x² + 1)e'dy = 0

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Q: Solve the equation [cos (2y) - (3x^2)(y^2)]dx +[cos (2y) - 2x sin 2y - (2x^3)(y)]dy = 0

A: To solve the given differential equation. First we check whether the differential equation is exact…

Q: Solve differential equation (2y cos y - x sec y - x tany)dy = (1 + sin y) dx

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Q: dx I [; (1-2x) I= [sin (4x) cos(4x)dx (In(x))3 dx I

A: Given

Q: äbäi 14 Q) Find dy/dx of the following :equation (x' +x)(x° - x +1) y = 17 KB/S dy/dx = - 4/x^2 O…

A: We use the Quotient Rule and  Product Rule of differentiation to find the answer of the given…

Q: dy dx a- 2e2y = ln x² b- y = (lnx+x)tanx d- y = ln xex 4) Find

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Q: 1- 2 - x = e»/2 x3 dy 2- (2xe + e*)dx + (x² + 1)e'dy = 0

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