(3y - 3y) Ay Consider the formo W=(3x* +2y) dx † And y =y dx %3D a6how that y is hot exact. 4)Find the anti-differential l for W- ) EValuate s W, where 6 ib the Gurve X = VI-t°

Q: Vydy 1+ y\y 3.

A: Soln:

Q: (y² +6y)dy (y+3)² 8.

A:

Q: dy Find y or for the following: 2x y - 10 = x* + cos y dx

A: We have to find the dy dx

Q: 5. y-2y+y-6e* d'y dy 6. 2. dx2 +2y e2x d'y dy 7. 2 -2y D4e 3x *

A: 5. givend2y(x)dx2-2dy(x)dx+y(x)=6exThe general solution will be the sum of the complementary…

Q: Find dy/dx and d^2y/dx^2.

A: Given

Q: + Use Separation of variables to solve eくX<| Us co,t)こ0 I4 pts] ULx,0) = X

A:

Q: 4. (3sin y- 5x)dx +2x cot ydy = 0 Ans. x'(sin y-x) = csin²y

A:

Q: Exexcises E Set 2] Implicit Differentia tion x=x 2. Find dy if dX 1. +Sin xy Find dy if 2x²- 3y'=8…

A:

Q: 5-find Аху : xe 12) if f(x, y) = xe

A: First I have mentioned what we have to find then just use the rule of partial derivative find the…

Q: (y? cos x – 3x?y – 2x) dx + (2y sin x- x'+ In y) dy = o

A:

Q: dx 7. = cosx cos² t dt

A: 7). To solve the differential equation: dxdt=cosx cos2t Solution: Re-arranging the given…

Q: 7. fa-4x')"x°dx

A: solution is given below

Q: QIFind dx /1+x²/3

A:

Q: Prove that (1-x*)у ,-ху, +р'у-0

A:

Q: (x’ – 10. 2x +3)dx x-4 c (4v+3)dy

A:

Q: Which of the following equations is NOT an exact equation? dy=0 B (xy - cos x)dx + (x² – 1)dy=0 (2x…

A:

Q: 2. f" S"(sinx + cosy) dx dy

A: Note: As per our company guidelines we are supposed to answer the first question only. Kindly ask…

Q: 3 y = Vlog2(sin5 x)

A: Given equation is y=log2sin5x3

Q: Evaluate dy/dx at x = 2 for the function below. y = 8u^2 + 3u – 4, where u =  7x^2 + 3x – 3

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.