fc y 3 ds, C :x=t2, y=2t, 0<t<1

Q: (ysinx + xycosx)dx + (xsinx + 1)dy = 0, with y(0) = 1 is %3D x*y? ++ = 9 3 3

A: Given that  The differential equation

Q: z 3e*3S,y 3z2 + sin(z)s G dx

A:

Q: t+1 dy If x = and y = t2 - 2t +3, then find t-1 dx

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Q: M-2-Sin(X y) nd dm dt X = t. yclint Z=et-1

A: Differentiation

Q: Evaluate /// (x + y – 5z) dV Where - E = {(x, y, z) | - 6 < y < 0,0 < ¤ < y,0 < z < x + y²}

A: The given integral is: I=∫∫∫E(x+y-5z) dV where E=(x,y,z) | -6≤y≤0,  0≤x≤y,  0&lt;z&lt;x+y2

Q: 3x sec (xy)dA; R={{x,y): 0 sxs7,0 sys 1}

A:

Q: 1. (x- v)dx+ (3x + y)dy = 0 when x = 2, y = -1

A: Let us first solve x-ydx+3x+ydy=0. So,            x-ydx+3x+ydy=0Let y be the dependent variable.…

Q: y*dx-(ay + y° kty = 0 Let the substitution v=2; y=vx; dy=vdx+ xdv

A: Given differential equation is y2dx-(xy+y2)dy=0

Q: d²y 1 dy y + y(3) = 0.009u, y(10) = 0.003s - dt2 t dt Use an appropriate method to find y(t).

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Q: Exact DE se: he particular solution of (x + y)dx + (x – y)dy = 0 when x = 1 & y = 1.

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Q: 8. (/E= + y² - y) dt + (y/E² – y? - t) dy = 0; when t = 3, y = 4 %3D

A: Solution is  ty=3(t2+y2)3/2 -363

Q: (* +y – 4z) dV where E = {(x, y, z) | 0 < y < 2, 0 < * < y, 0 < z < a +y?} Evaluate

A: ∫y=00∫x=0y∫z=0x+y2x+y-4z dz dx dy Now, ∫z=0x+y2x+y-4z dz =x+yz-2z2z=0x+y2 =x+yx+y2-2x+y22…

Q: d²y Find the solution to the IVP dt2 dy + y = 0 where y(0) = – 2, dy (0) = 5. dt y(t) = Preview

A: Steps are follows . Auxiliary equation and solution of the equation . General solution . And values…

Q: 4 J4- y ktx dy S[S( x, y) dA = [] 3 R 0 2- 2 2

A: Consider the given expression, ∬Rfx,ydA=∫04∫2-y24-yx2-x33dxdy This suggests that the region spans…

Q: w = In(x²+y² +z²) x = cost y = sint z = 4E

A: w=lnx2+y2+z2, where x=cost, y=sint, and z=4t. Find dwdt.

Q: ) 3(x+ y) dx + x(x*+ zy + uy) dy - o t.

A: We’ll answer the first question since the exact one wasn’t specified. Please submit a new question…

Q: 1. Separating the variables dy 1 x(y- 3) =D4y dx %3D

A: In the separation of variables method of solving the differential equation, the different variables…

Q: y² + 5 dy J y²Cy² + 25)

A: Given problem:-

Q: dy Find a solution of x dx y2 - y that passes through the indicated points. (a) (0, 1) y = | 0

A:

Q: Evaluate //| (x + y – 2z) dV where E = {(x, y, z) | - 2 < y < 0,0 < x < y, 0 < z < x + y²}

A: A detailed solution is given below.

Q: y' + 4y = e^(4t) %3D

A:

Q: y'dx-(sy + y* }ky = 0 1. Let the substitution y=2; y=vx; dy=vdx + xdv

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Q: (ztan 2 +1) dx – x dy = 0

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Q: Find the solution y = y(x) of dy y2 +y dx 0, x3/2 subject to y(1) = 1.

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Q: d²y 35. Find dx2 of x² + y2 = 1 implicitly. %3D

A:

Q: dx Find the value of at y=1 if x=z³+4z and z= dy (y? + 2y)²/3.

A: Given,         x=z3+4z  and  z=y2+2y23

Q: LLL- (x+ y+ z)dydxdz. -1 J-1 J-1 |

A:

Q: Y" - Y = { 2, %3D Ost Y(0) = Y'(0) = 0, %3D %3D t21

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Q: 4. (x + Vy? + 1)dx-(y y-: dy = 0 Vy2+1, %3D

A:

Q: dx Find the value of at y-1 if x-z+5z and z= dy (y? + 2y)2/3.

A: x=z3+5z  &amp;  z=y2+2y23 Now put z=y2+2y23 in x=z3+5z, we get x=y2+2y233+5y2+2y23⇒x=y2+2y2+5y2+2y23…

Q: y" + 2y' +4y = u(t)*e^-(t-2); y(0) = 0, y'(0) = -1 , find L{y} (= Y(s) ).

A:

Q: C:x=t4, y =t (-1<1< 1) 25. -ydx +x dy C : y² = 3x from (3, 3) to (0, 0)

A: First I have change the line integral into single variable using the given path and taking limit…

Q: 3. (y – 2)dx – (r - y – 1)dy = 0 (coefficients linear in two variables) %3D

A:

Q: dy Va2-x2 with initial condition y(a) = 0. dx -a va2-t2 dt This can be solved by y = J %3D II

A: From the above question, we get the differential equation dydx=-a2-x2x with the initial condition…

Q: 2. Find the solution (implicit or explicit) dy (y+1) = 3sin(x). y(7)= 2 dx %3D

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Q: y - cx°y' +e + sin(xy) – (ny+ y@) =0 -ху y' =?

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Q: u2-1 Given y = dy and u = Vx2 + 2, find dx %3D u3+1

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Q: ii- (x* + y) dx - ry dy = 0, y(2) = 1 (using Integrating Factors)

A:

Q: السؤال الأول: جد باستخدام التحويل x = rcos(0( , )0)V3rsin y = ناتج التكامل و ] x)>و dxdy 0.

A: We have to use polar coordinates integration.

Q: sec y Then y8 Let z dz dy y16

A:

Q: y' = x+y+xy, y(0) = 1 at the point x = 0.1 (h=0.02) Use 4th order RK

A: Given y'=x+y+xy where y=1 when x=0. The objective is to find y0.1 using Runge-Kutta 4th order…

Q: – 4z) dV where E {(x, y, z) | 0 < y < 1,0 < x < y, 0 < z < x + y²} Evaluate + Y E

A: We just need to put the limits and then integrate as following

Q: Evaluate: [S y² dV where E the solid hemisphere x² + y² + z² 0

A: We have to evaluate the triple integral ∭E y2 dV on the solid hemisphere x2+y2+z2≤9. Observe that…

Q: 2x? dy 2 - y dr dy = cos z dy x + y dr dy 3x O dy E = y (2 – y) ||

A: The given options are  y'=2x2          (1)y'=2-y         (2)y'=cosx       (3)y'=x+y…

Q: Approximate y(1,5); dy = 2x; y = x²; Step size: h = 0.1 dx

A:

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.