11T |13T V2 - V6, determine the value of sec 60. Given that sec 12 %3D 12

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Q: Find the complete solution of d dt 5t Vs

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Q: Exercise 3. compare the values of dy and Ay in each case (3a) y = 0.5r" I = 2 Ar = dr = 0.1 (3b) y =…

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Q: Solve the D.E 9+4y = Sec2X %3D

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Q: a) sec²t + dt 2 + V5 b) ys – 2y c) - dy

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Q: 5 2 11 what is 3 Given that f(æ)dæ : f(s)ds?

A: We will use the following 2 properties of definite integrals to find the answer

Q: 26. у" + 4y' %3D sec 2x

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Q: (금)시 3 k dt t2 (5 – 5t)i + 4/tj+ -

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Q: For y''+3y'+2y=e^-x, use the variation of parameters formula to find a particular solution. Show…

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Q: a) Find the general solution for UTM dy TM dy +2- dr? dr (1+f) UTM (77 +1)xz² = fip +

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Q: Let z=xIn(x²+y²-e)-235xy, x=te, y=est. If the value of oz when s=2 and t=1 is equal to Ae?+Be", then…

A: Here, the given functions are: z=x lnx2+y2-e4-235xy, x=t es, y=est so, z is a function of x and y…

Q: (m² + a² + 1)dm + m(m – 2a)da = 0 | %3D m2 Option 1 O Option 2 m-1 m2 Option 3 O Option 4

A: The given differential equation is; (m2+a2+1)dm +m(m-2a)da =0.

Q: The general solution to d?y/dt2 = 25y is

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Q: Solve using variation of parameters or reduction of order (D² – 3D + 2)y = (1+e²x)¯2

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Q: Solve the non-homo. D.E. 1.y" + у%3D Зе2x

A: Differential

Q: 3 '9-x2 3+V9-a2-y? 1 dz dy x² + y² x²+y² a C = L7I Fle,0,6) dp dộ do

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Q: e 12t dt 31. 4et -1

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Q: (t5 + 1)dt dp 3.

A: ∫3xt5+1dt =t66+t3x =x66+x-366-3 =x66+x-2492

Q: Find the complete solution of the DE (D3+6D2+11D+6)y=ex +cosx.

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Q: Ex: FIND A COMPLETE SOLUTION OF EQ. y" + 3y" + 3y' + y = 0

A: The given differential equation is y'''+3y''+3y'+y=0. Find the complete solution of the differential…

Q: If find the value of a. 3 S₁ S² (x + 2y) dydx = 10, 0 a

A: Given: ∫01∫a3(x+2y)dydx

Q: by first – shifting find L(e2t t3)= %3D 6. (s-2)4 .a O 1 (s- 3)4 .b O (s -2)3 3 (s - 2) 4

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Q: 3 9 dx dt -1 -3 2 and x(0) 4 ||

A: In the question it is provided a system of differential equations:

Q: (4) (b) 10tsin(5t²- n/4)dt (4) (c) S 12(x³ + 2)ex¹+8x dx

A: We have to evaluate the integrals.

Q: Solve the Bernoulli's DE: 2x3 y = y(y? + 3x2). %3D

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Q: af If 2xy(-x² + y) + xe", what is ду ду? Select one: а. 4ху — 2x3 + хеУ ду? 2x(-x² + 1) + xe" b. ду?…

A: Given ∂f∂y=2xy−x2+y+xey

Q: Solve the IVP y + 2y = 0 if t≥ 1 y(0) 1. Is the solution continuous? = "

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Q: d³x d2x dx -2- =0 dt dr3 dr?

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Q: Evaluate the integral

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Q: 2d) Let a e R find the solution of y' (x) – ay(x) = 0

A: as you didn't mention question number to be solvedso I solved first question. For Further solution…

Q: 3. p + y = ty dt dy 2ty(y – 1) dt 6. 3(1 + ²) %3D

A: Given 3 t2dydt+y2=ty6 31+t2dydt=2tyy3-1

Q: What is the general solution of ху(ху5 - 1) dx + х?(1+ ху)dy3D0 ? A 2x3y5-3x² = cy? B 2x°y3 - 3x2 =…

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Q: Use the method of variation of parameters to solve the following y + 4y + 4y e- In z, z>0

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Q: S(2 + e2*)³dx

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Q: V9-r² S xydzdydx •3 (d) S So

A: We have to find value of given triple integration

Q: Find the value of 3t dt 0. O a. 4/3 O b. 2/3 O c. 1/3 O d. 5/3

A: A detailed solution is given below

Q: Find the su x² + y? :

A: The surface is given as z=xy. Take the derivative of the surface, z=xyfx=y, fy=x. The surface area…

Q: 3(1 + P) = 2ty(y³ – 1) dt %3D

A: Let us consider the differential equation dydt+P(x)y=Q(x)yn It is known as Bernoulli's equation…

Q: dy + ydx %3D = 3x²y?dx,

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Q: Q16 3 a) / 3²+ 2dt dt c) /,₁ (3-5)²

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Q: What is the general solution of differantial equation?  Whicf of the options x² - y² + xy dy/dx =0

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Q: A. Using the basic formulas, integrate the following: 1. fx(x² +2)²dx 2. S(2V – 3x)²dx 3. fx³Vxdx 4.…

A: Note: As per our guidelines we are supposed to answer only 3 sub parts under one question. kindly…

Q: Find the value of k so that the value of (2y - 1) dy is 10.

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Q: Find positive numbers x and y satisfying the equation xy = 16 such that the sum 2x+ y is as small as…

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Q: (a) In e7 (b) eln 2 %3D (c) eln v3 %3D Preview (d) In e5

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Q: 2ste-tds + (s²e-t – t)dt = 0

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Q: f Lan 2X e *3 of +sec2X Pinel dy o

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Q: 2 4 Mx(t) = -e+ 3t e' + e" + %3D 3 15

A: Given: Mxt=13et+415e3t+215e4t+415e5t

Q: Minimize c=s+ 2t subject to 4s +t2 270 2s +t2 190 s+ 3t 2 330 s20, t2 0. C = (s, t) =

A: The given minimize problem is C=s+2t subject to constraints, 4s+t≥2702s+t≥190s+3t≥330s≥0, t≥0   Then…

Q: Determine the value of C if f(x,y) = C is the solution of (x+ 2y-3)dx+(x+2y+1)dy3D0 for x=94 and y=…

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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.