X Coy-Ycor I+ Sinz +Siny

Q: cos’x sin x dy + (y cos³x – 1) dx = o %3D

A: We have to find the solution of given differential equation

Q: y = (sin x)e¯* find de sin-1y %3D d In x

A: y=sinxe-x. Then we have to find desin-1ydlnx.

Q: Integrate S(cos x)e*+sin xdx B. et-sinx + C A. -e4+sin x + C c. e4+sinx + C D. e-4+sinx +C A В C D

A: Given: I=∫cosxe4+sinxdx  ....(1)   We know that; ∫eax+bdx=1aeax+b+C

Q: J cos x sin x V1 + sin² x dx

A:

Q: X Sinx cos k dy 0. COs

A:

Q: xy sin y dAR: - 3sXs3, 0sysn SSwsiny dA= xy sin y dA =

A: Use double integration to evaluate it

Q: 1 + cos x – 2xy): fip y(y + sin x), y(0) = 1. COS I 1+ y? dx

A: To solve the given exact differential equation.

Q: z = 2e"žsinx – 3e*cos(y) Ве find: www a²z a2z (n az а) дхду"") дудх ,b) ду

A:

Q: a. sin y i + cos x b. хyz (хі+уј+zk)

A: Note that : Curl of the vector field describes it's rotation.

Q: (sinxy +xy cos xy) dx + x² cosx y d y = о

A: The solution is given as

Q: sin x dy 2. dx 2у x2

A: In this question we have to find the solution of the given differential equation.

Q: 7 Find dy (b) x siny-ycosx-y = 1. dx

A:

Q: Using Variation of Parameters 4y''+4=cos-1x

A:

Q: siny µ(x,y) = ye* is an integrating factor of dy 3D0 2e sinxldx cOsy+2e COSX Select one: True False

A:

Q: sin(x) sin(y)dx + cos(x) cos(y)dy = 0, y (0) = 2, h = 0.5, Find y (1) using fourth-order RK

A: 4th order RK method  yi+1=yi +16k1+2k2+2k3+k4Where ti+1=tn+h          k1=fti,yi,…

Q: Original Sound ff EXERCISE dy -x = x2 siny dy 3 -(-siny ANSWER: X = %3D

A:

Q: ODE dy = sin (x+y) √x

A:

Q: 3. + x° siny-y と3 cOS C fond C Frc foeと y g りな in) fy

A:

Q: (siny – 2ye*sinx)dx +(cosy + 2e*cosx)dy = 0

A: Given differential equation (sin y -2ye-x sinx ) dx+ (cosy+2e-x cos x ) dy=0

Q: sin y(x + sin y) dx + 2x² cos y dy = 0.

A: Given equation is  siny(x+siny)dx+2x2cosydy=0

Q: siny dx + (x - sin? y)dy=0

A: Here, we will differentiate  siny dx+x-sin2ydy=0....(1)

Q: sin³ y dy 2. S 1- siny

A: Solution Given   ∫sin3y1-sinydywe need to find the integral

Q: sin(x) sin(y)dx + cos(x) cos(y)dy= 0, y(0) = 2, h = 0.5, Find y (1) using fourth-order RK

A: We have to find y(1) using fourth-order RK.

Q: dy cos(x)–+ y sin(x) = sin²(x) cos(x) y³ %3D dx

A:

Q: y = Vr² + VT etin e y = r-5 y = (cos z)n. y = /tan 2x – sec3 (4x – 1)

A: as we are just given 4 functions and not any question so I assume we need to find the derivative of…

Q: cos y – sin y dy 1+ sin(2y)

A: Given: ∫cosy-siny1+sin(2y)dy

Q: (sin y – y sin x)dx + (cosx + x cos y)dy %3D

A: siny-ysinxdx+cosx+xcosydy=0An ODE Mx, y+Nx, yy'=0 is in exact form if the following holds:1.  There…

Q: sinx siny dx + Cosx cosy dy = 0

A: Given: sin⁡xsin⁡ydx+cos⁡xcos⁡ydy=0 ⇒sin⁡xsin⁡ydx=-cos⁡xcos⁡ydy ⇒dydx=-sin⁡xsin⁡ycos⁡xcos⁡y…

Q: I) sin X dy dx Sin 2X - y Cos X

A: Explanation of the answer is as follows

Q: siny dx + (x – sin? y)dy=0

A: We have to solve the differential equation sin y dx + x-sin2y dy = 0   We know that ∫cosec x dx =…

Q: (sinx+1) y = (cosx+1)' dy evaluate dx

A: We have to find the derivative

Q: 3 y = Vx +=+ sinx %3D

A:

Q: dx Vx Vx (1+Vx)2 •Tt/2 3 3 S/2 3cos® (x)sin?(x)dx S sec³ (x) sin³ (x)dx

A: Explanation of the solution is given below.....

Q: (cosxcosy – cotx)dx – sinxsinydy = 0

A: Given equation cos x cos y-cot xdx-sin x sin y dy=0  ......1 If a differential equation is in the…

Q: 2- y" + 4y' + 20 y = 23 sin t - 15 cos t y(0) = 0 , y'(0) = -1 %3D

A: Differential equation is, y''+4y'+20y=23sint-15cost Given conditions is, y0=-1y'(0)=1

Q: F(x, y) = 3x – 4y3 + 5x°ys + cos(x) – 3 sin?(y) |

A: Given query is to find the partial derivative onnf the expression.

Q: 5 (2xy* + sin y) dx + (4x²y³ + x cos s y) dy = 0 %3D

A:

Q: sin x sin y dx + cos x cos y dy = 0

A: Using variable separable method.

Q: 4) sin x sin y dx + cos x cos y dy = 0

A:

Q: Q4. Test for exactness and solve (ycosx – cosy)dx + (sinx + xsiny)dy = 0

A:

Q: 4. f(x,y) = sin²(x – 3y) %3D

A: It is simple partial derivative

Q: e) cos (x + y) - cos(x - y) =-2sinxsiny

A: The LHS of the given equation is cosx+y-cosx-y. Note that, cosA+B=cosAcosB-sinAsinB and…

Q: (v sin' 2) dn sin ædy

A: This is a question of exactness, non homogeneous differential equation.

Q: b) x siny-ycos x- y = 1.

A:

Q: dy - x = x2 siny dx 3 -2 (-siny + cosy + Ce-y/2)* ANSWER: x = -

A: Note: Here, we shall solve Bernoulli's differential equation  dxdy-x=x32sin y instead of…

Q: 3e7" sin(2y) 3e7 sin(2y) dy

A:

Q: 9. (siny - ysinxy)dx + (xcosy-xsinxy)dy 0

A: note : as per our guidelines we are supposed to answer only one question. Kindly repost other…

Q: sin 2ydy 5.J7-3 cos 2y 15.

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.