12. Use separation of variables method to solve du u> x > 0 subject to u(0, t) = u(n, t) = 0 for t>0 = sin? r for 0

Q: dx 1)y /sec(3x) 2) y = Vu + 2u , x= u? - 3u

A: Definition used -            Chain rule of derivative -                             ddx(f(g(x))=…

Q: 3) Find dy dx a) y = x+In(sec 3x) %3D In(x+)

A: solution:-

Q: dy B) Find for all the following dx 1) y = sin-13x 2) y = In(5x) 3) y = Vtanhx

A: Solution: As per our guideline we are supposed to answer only first three question please repost…

Q: tan²xdx = sin³ydy when x = 2, y = 3

A:

Q: 11. Integrate the function. y? -dy (49 – y² ) 5 y 7y +C - sin"' y + C V49 – y V49 – y² V49 - y -…

A:

Q: y" + y = sec x tan x

A:

Q: Find y' where y = tan(11a? + 8) v173 + 17 Answer: 51a2 y/ = sec2 (22æ)\/172³ + 17+ tan(11a² + 8)…

A: I have used the rule for composition of function and multiplication of functions

Q: Solve "-4y + 4y = con t w(0) =1 lv(0) = 1. " sint +cont-int vit)- v(t) = ce' cos 2t + cge" sin 21 +…

A: I am matching with particular integral. But no matching option is found

Q: Find the general solution of the system of equations 2 -5 x' 0 = - ( ² = ₂ ) x + ( cost), 0 < t < *.…

A:

Q: If u = x3 -3xy and v= 3x2y-y3, prove that Pu/Əx2 + Pu/əy2 = Pv/ax2 + Pv/@y²

A:

Q: Find nd cos(z ² + y²)dA where D = {(x, y) | 16 ≤ x² + y² ≤ 81} D

A:

Q: How did he get the value inside the circle f(x, y)=x² + sin(xy) Vf=x*+sin(xy)) i+ d(x²+sin(xy)), dx…

A: given ∇f(1,0)=2i+j we have to find the direction in which the directional derivative has some value.

Q: y" + y = sec x tan x

A:

Q: Hiw 2 Find dy For (πCシ)

A: Differentiation of the function helps to find the derivative of the function. Simplification of the…

Q: dy if 6 + sin 2y = dx 2y + 3x by using implicit differentiation. 2y + 3x Find Hence, find the…

A:

Q: tan x= Sin 2X

A: Given: y'+y tan x= sin2x

Q: Solve dy dx Option 1 - y tan x = -y² secx 1- y = sec² x + tan x + C 3- y = secx + tan² x + C 2 y-¹…

A:

Q: 2. Solve for y in the equation y = e* sin x + e* cos x – y +c 3. Solve for f e* sin x dx in the…

A: Given, (2) y = exsinx +excosx -y +c  We have to solve for y (3) ∫ex sinx dx = ex sinx + ex cosx -…

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

A: Note: As per our guidelines we are allowed to solve one question

Q: ) Find the slope of the curve x +y3- 6x²y = 0 at x = 1

A: Slope of a curve: For non- linear functions, the rate of change varies along the given curve. So,…

Q: Find the general solution of the differantial equation given by www |y" – 4y' + 5y = 3xe* – cos2x +…

A: Given y''-4y'+5y=3xex-cos2x+x+1sin2x

Q: -(v/y)- o None of the above () ferentia uation y"+y' = 1? What is the general solution of the dif-…

A: given differential equation :-             y''' + y' = 1

Q: y" + y = sec (x)

A:

Q: Solve the following 1 1) y dx + x² + y? dy = 0 x +y 2) (3x? In x+ x² –y) dx- xdy = 0, y(1) = 5 dy…

A:

Q: /Prove that the value of cos()dz, when z = T + 2i is e + e-1

A: Complex integration of the function

Q: Q4) Use separation of variables method to solve: d²u ди ax² + =u where u(0, y) = 0 and ду du(x,0) by…

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.