4) Solve: a²u at² dx4 = 0 00 u(0,t)= u(L,t)=0 t>0 Uxx(0,1)=Uxx (L, t) = 0 u(x,0)=x sin 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: Show that y = -cosx In(secx + tanx) is a solution of y" +y = tanx

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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: Hiw/ Find F'(x) 1. if F(x) = x, tanx 2-if y = Sinx it casx 3- Find g" ()if y co) = Sec y ex) g ex)…

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Q: find dy/dx y = | Vx V 1 5) 1+x 20) y=Cof"| 1-x, 15) y = \tan /2x + 7

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Q: au at a²u 28. Solve Əx² U(x, 0) = 3 sin 2+x, U(0, t) = 0, U(1, t) = 0. = where 0 0 together with…

A:

Q: tan y dy + In (secy) In (6)sec® de

A: Given data:     The given integral is: . The given integral can be written as, Assume Let…

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

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Q: Find directional derivative for f(x,y) = y +, Xo = 4, yo = 5, nx = 1, ny = 0. df ðf af -Nx + -Ny=|…

A: We will evaluate the required values.

Q: Hiw/ Find F'(x) 1 x, tanx if F(x) = X 2-if y= Sinx 3-Find y" (I)if yex) = Sec

A:

Q: If f(x)=14-x^(2) and g(x)=\sqrt(x+31), compute g(f(3)). Simplify your answer as much as possible.

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Q: Use a suitable method  to find the solution of (1-x^2)(1-y)dx=xy(1+y)dy

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Q: Find general solution of ODE   (x+y-1)dx-(x+y)dy=0 dy/dx = (x+2y-3)/(2x+y-3)

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

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Q: find dy/dx 4x -x 2x 23) y= Sin- +x².Sec 2-x + 2x.Sec) 2 (ans.: (2-2»N(2-x² - x* 4 4

A: To find the dy/dx means y' of the given function

Q: A spacecraft has acceleration r"(t) = , initial velocity r'(0) = and initial poition r(0) = (0, 0,…

A: GIven that a spacecraft has acceleration with initial velocity r'(0) = <2, 5, 1> and initial…

Q: a) Find dy if y² + x²y² = 1+x^y use implicit differentiation b) If x² + y² = 6. Find y' in term OF…

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Q: x2 + 8x +3 10) y=- _ dy A) 3x2 + 8x - 3 dx X Find the derivative. A) 11) s= t3 tan t-√√t ds dt C) dy…

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Q: Use the rule for recipocals : f '(x) f?(x) d 1 dx [ f(x) to find the following derivatives…

A: Given: Reciprocal Rule: ddx1f(x)=−f'(x)f2(x) Find: 1)  ddx1x2+2x+1=?2)  ddx1sinx+ex=?3)  ddxπx+1=?

Q: 4. a) Find the general solutions of the following differential equations. Express the general…

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Q: Solve F'(t) = t+ F(t – u) cos u du, F(0)-= 4. %3D

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Q: find dy/dx x(х+1)(х- 2) (х*+1)(2х+3) 25) у%3 43) у%3D 1+(lin x)? 1+(ln x)?

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Q: Harry fills up his Jeep with gasoline and notes that the odometer reading is 23,511.9 miles. The…

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Q: (2x sinh2 + 3y cosh?) dx – 3x cosh dy = 0 |

A: Concept Used: For  y'=f(x, y)   ...(*)If f(hx, hy)=hn f(x, y)Then (*) is homogenous equation of…