L{t sint cos t} %3D (A) 4)2 (s2+4)² -2s (B) (s²+4)2 (s2+4)? 28 (D) (s2+4)2 (82+4)2

Q: 3. f(t) = 2e3t sin 2t – 3e3t cos 2t -

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Q: Find impicitly, tf e*(eУ — 1) + sin(2x + 5у) %D In(V7) - - сot(2x) y+2

A: Given function is Differentiating with respect to x by using product rule ,we get

Q: is a solution of y' =y sinx. -COSX y =V2 e Select one: O True O False Jump to...

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Q: find general Solution (D²+6D. Sin 4X to

A: Given differential equation is : D2+6D+16y=sin4x To find the general solution.

Q: D6 – 6D5 – 4D4 + 18D³ + 5D² – 14D + 13y = 60cosx + 26 + 2v = sin (e-x)

A: We have to find the general solution of the given differential equations

Q: y" + 2y' = 4x – 5 cos(x).

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Q: (D² – 10D + 34)y = -cos3x

A: First we find complementary function then find particular integral.

Q: +3x2 B) Find dy/dx if : (****")) (v)² = sin (cos³

A: Differentiation chain rule

Q: 5*-1 a) If y =Vx* +sin (5x)+ 2 then dy fınd dx b) If y = e2*sinx, then show that d²y =…

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Q: Q3.lf f(x,y) = sin²(x-3y)+sin(xy find: and af dy ax

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Q: Q4) Choose correct answer : rtan-(cotx) dy dx = i) So 10n а. 44 15n b.- 44 20n С. 44 d. 1-n 2

A: Given: ∫01∫0tan-1cotxdydx

Q: Q4) Choose correct answer: 1 csin-(cosx) dy dx = 1-п а. 1-n b. -2 1+n С. 2 1+n d. -2

A: The given expression is ∫01∫0sin-1cosxdydx.

Q: e" sin°(2x) (d) y = In 2x2 + 1

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Q: Q2/ if y = Jsec3 /sin+Vx+ x² 4. find y'

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Q: The sales of shirts and ties at a store are related by the equation 0.6x + 3xy + 8.3y = 78659.1,…

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Q: using undetermined coefficients (D^2-2D+2)y=24e^x sin3x

A: Given: (D2  -2D+2)y=24ex sin3x

Q: (D² – 2D - 3)y = 2sin x a. , =cosx -sinx =-cosx -sinx c. = -cosx +sinx COSX 1 b. yp С. Ур 21 COSX d.…

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Q: (D² + D)y = 81r² +14 cos(4x) where y(0) = 0 and y'(0) = 3 %3D

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Q: (D³ + 3D + 4D³ + 12D²) y = 32 cos (2x) +3e3 – 16 sin (2) -

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Q: Q4: Find by using udv method cos bx dx ax

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Q: f(t) = t² cos 6t 2s(108-s2) 2s(s²-108) А. (s2-36)3 C. (s2-36)3 2s(108-s?) В. (s2+36)3 2s(s?-108) D.…

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Q: (D² – 2D- 3)y = 2sin x a. y, = -cosx – 2 sinx =csx COSX b. y, = --cosx - - sinx COSX c. Y; = - cosx…

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Q: (cos y + Gxy3) dx + ( 2kx³y²-x any)dy=o

A: We are asked to find the value of k

Q: L sinh-t %3D .a 3s2-4 6. .b O 9s2 -4 .c O s2-4 3. .d O 2s2-4

A: We know that  L( sinh(a)t) = (a)/(s^2 - a^2)

Q: I Solve the fllowing FODF 2y(x+y+2) dx + (y²-x²_ 4x-1)dy = o when x=2,y= 3

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Q: (d) y' + 2 sin 2nx = cosh 3x %3D

A: As per our guideline we are supposed to answer only one asked question.kindly repost other question.…

Q: fCx) at c0,2) で +x + co.2) 2. メ 2/3

A: Given curve is fx=23x2+x+2. To find the equation of tangent line and normal line of the curve at…

Q: Find L S e2a sin (3t – 3a) da ta] 3. A) F(s) (s-2)(s² +9) -3 B) F(s) : (s+2)(s² –9) 3s C) F(s):…

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Q: Q2) Solve (y+ysin x) dx - (cosx- 2xy +) dy = 0

A: Given differential equation is  y2+ysinxdx+-cosx+2xy-1y2+1dy=0 Comparing it with Mdx+Ndy=0, we get,…

Q: 3. f(t) = 2e3t sin 2t 3est cos 2t %3D -

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Q: solve linear DE (D2+2D+2)y=e-x+sin2x

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Q: Q4: Find by using udv method ax cos bx dx

A: Here I am attaching image so that you understand each and every step.

Q: (D5+3D + 4D³ + 32 cos (2a) + 3e 12D²) y = 16 sin (2x)

A: The given differential equation is…

Q: Q16 a) / 31 3t+2 b) dr cos² a √5+tanz » /; c) [₁² dt (3-5t)²

A: Given :(a) ∫3t3t+2dt(b) ∫dxcos2x5+tanx(c) ∫12dt3-5t2

Q: (D² – 2D + 1)y = 2sinx 2 Yp= Ур = 2sinx · Yp = = COSX Ур 3 Sinx- 2cosx Yp = sinx+ COSX

A: I have used the rule for finding particular solution and find that  Option (B) is correct.

Q: 6. (D2 – 6D + 8)y = e2x + sinx %3D

A: The given differential equation is: D2-6D+8y=e2x+sinx   So, the auxiliary equation is: m2-6m+8=0

Q: y² + 3y - +3y² -2 = e. Sint by varition Method

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Q: Q21// find the general solution (sin²x + 2ye²x + 2)dx + (e2x – sec²y) dy = 0

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Q: (4D3 + D)y = e2* A. y = c1 + c2 cos 0.5x + c3 sin 0.5x +e2x 33 B. y = c1 + c2 cos 2x + c3 sin 2x…

A: From the given problem: 4D3+Dy=e2x The auxiliary equation is: 4m3+m=0m4m2+1=0m=0  or…

Q: 3 f²f²² ²³ y cos(z³) dx dy dz 0

A: The given integral:∫01∫0z2∫03ycosz5dx dy dz

Q: (D² – 3D + 2) y = 14 sin 2x – 18 cos 2x

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Q: z) tan(y2 + %3D

A: Given that, wx,y,z=tany2+4zx3x=r2t2y=r2tz=rt2 Then we get,…

Q: Q2) a) Find an® sec²y dy b) Is cos4xv2-stn4x dx = (2- sin4x) +Ctrue or false? show me

A: Use fundamental theorem of calculus for part (a)  For part (b) use substitution method

Q: 11. (D² + D – 2)y = 2x – 40cos (2x) 12. (D? + D)y = -cosx

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Q: Q1. L{t sint cos t} = (a) 8 (b) (3²+4)² 2 (c) (d) -2s (8²+4)2 2s (s²+4)² 2 <-8 (s²+4)²

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Q: - (D² +2D+5)y=e* sin 2x

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Q: S-* cos(x²)dxdy = Q2): Show that 1-y2 %3D 6.

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Q: x² (d) S √1-4x² (HINT: sin² t = dx. (1. (1 - cos 2t).)

A: We have to evaluate ∫x21-4x2 dx.

Q: Q1: Solve the DE d³y dy x3 +x dx3 = x Inx cos(2lnx) by using inverse dx operator method.

A: To Determine :-  The given differential equation  x3 d3ydx3 + x dydx = x lnx cos2lnx by using…

Q: (D3 + 2D2 – 16)y = 40e2x + 80 sin(2x) %3D

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Equations and Inequations

Equations and inequalities describe the relationship between two mathematical expressions.

Linear Functions

A linear function can just be a constant, or it can be the constant multiplied with the variable like x or y. If the variables are of the form, x2, x1/2 or y2 it is not linear. The exponent over the variables should always be 1.