10. Jljul * If µ(x, y) = x" y"is an integratingfactor of the the DE. (12 + 5xy)dx + (6x y + 3x²)dy = 0 Then, the values of п аnd m are O n = -3, m = 2 On = -2, m = 3 O n = 2, m = 3 O n = 3, m = 2 O n = 2, m = -3 O n = -2, m = -3 On = 3, m = -2

Q: he following function: =: Find fxy. f(x, y) = 5x4y6x4y5 - 21

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Q: ,3 хуз 1. у' 3 V1+x2

A:

Q: 12. integrate (10x+6x +2x-6)dx

A:

Q: 8. Integrate S –x³Vx² + 2 dx

A:

Q: 4) (e* + y)dx+ (2y + x)dy = 0 %3D

A: Hence, the general solution is                                            y=-x±x2-4(ex-C)2 Where C…

Q: what value of n can be used to transform the Bernoulli equation y'+p(x)y=q(x)y^n into an equation of…

A:

Q: integrating x and xy' - x 12 = ?

A:

Q: Find y'' for y = 4+ 5X 3

A: Given :   y=4+5x3     To Find : y''

Q: The integrating factor of xdy + ((3x + 1)y – xe-2*)dx = 0 is %3D O a. xe* O b. 3xe* O c.x'e* O d.…

A: given :

Q: What is the general solution of the following ODE y' - (2y/x) = 3x3 Hint: Use integration factor…

A:

Q: 25) y'=} +2y yl

A: We separate the variables first

Q: ind the general solution for  Z_yy +Z=e^(x+y)

A: zyy+z=ex+y

Q: 1. S 3x° + 2x3+7x - 4 dx 2. Sx7 – 48z11 3. S 10t-3 + 12t-9 + 4t³ dt 5z16dz -

A:

Q: If y = u^4 − 2u^2 and x = u^2 − 2u then find d(y)/d(x)

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Q: 7. If g(4) = 3k +7, g(9) = 7, g' is continuous and %3D J g'(x)dx = 2k? + 13, find the value of k.

A:

Q: Determine the uncertainties in x2 and y2 using the rule for propagating uncertainties when…

A: We need to Determine the uncertainties in x2 and y2 using the rule for propagating uncertainties…

Q: What is the solution of the given ODE xy' + y = Vx

A: Given: xy'+y=x

Q: 3. x'= -2tx + y, y'= 3x-y

A:

Q: find a particular solution to: y''+5y'+4y=8te^(2t)

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Q: b y' = 2 + ₁e-ax a

A: details steps are given in step 2

Q: For S(y + 2) /2 –- 3y dy,y = O y = u^(1/3) O y = u^3 O y = u None of the choices

A:

Q: Are these equation separable 1.s2+ds/dt = (s+1)/st 2.dr= b(cosx dr+ rsinxdx) 3.y'=ye(x+y)/(x2+2)

A: The objective of the problem is to determine whether the given equations are separable. A…

Q: (1 + Iny-) (;++i" y) dy = 0; 7. dx + y(2) = 1 Ans: In y+x+xIny-=0

A: The given differential equation is  1+lny-xy dx + xy+x22y2+3yln2y dy =0   ;  y(2) =1 Compare with…

Q: find dy/dt Y= (1+cos4t)^5

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Q: 5. x' = 3x - y, y' = x + 2y

A:

Q: Find the general solution to the following Bernoulli Equation: dy/dt - 3 * sqrt(t) * y = sqrt( t *…

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Q: S t /1+3t - dt

A:

Q: and d^2y/dx^2 for

A:

Q: find general Solution of DE. 4xg dx +x'dy +3y°dx +2xydyexd

A: The objective is to find the general solution of differential equation 4xydx+x2dy+3y2dx+2xydy-xdx=0

Q: Show that y = e^2t is a solution of y’’’ - 2y’ - 4y = 0 (where ‘ denotes d/dt), and find the general…

A: We need to solve differential equation and show that y = e^2t is a solution.

Q: Find ect and the solution to X' = CX + (1) t X (0) = 0

A: X'=CX+1t1X0=000

Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.