Q3. Evaluate 2m sin2e de 5+4cose

Q: y" + 4y = 16t sin 2t

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Q: (D2 + 9)y = 30 sin 3x

A: The differential equation D2+9y=30sin3x, we have to find the solution of the given differential…

Q: dy. =Cosx-Sinx t4 6くしく o-5, 0.52

A: The given initial value problem is,dydx=cosx-sinx+y,   0≤x≤0.5, y0=0To solve this using fourth-order…

Q: 3. What we want to do next is write (x + jy)as Relº where R = (x2 + y² ) and tan-1(0) = (2)

A: If you have a complex number z = r(cos(θ) + i sin(θ)) written in polar form, you can use Euler's…

Q: 1. (D² + 30+2)y=24 cos 3x

A: First we find complementary function then particular integral and then general solution as in next…

Q: d'y 6. if y =, dx² 1-cos4x 1+cos4x du

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Q: fx) = Зх - 4 at (4, 2) d y=x In x at (0, 1) sin3x y = 4 at T 2

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Q: 4 ry sin (x? + y*)dxdy Find

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Q: d'y For y= 2cos +5sin x, if =m sinx+n cosx, dx2 then 2m+n=

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Q: Q3\ find General solution of sin (xy). (ydx + xdy) = 0 %3D

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Q: a) y = 2cos?t+2 ; x=(r* +3)' b) y= 5te" ; x=4e c) y=(3t sin 3t – 1)* ; x= 612

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Q: Evaluate | (3t + t²) sin(2t) dt

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Q: ~2y 2 Evaluate 8 sin y dz da dy.

A: You need to have the idea in which order these integral should be solved.

Q: H.W Find y' for y = ecosx tan (5x) * (5x? + 1)?

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Q: is a solution of y' y sinx. -COSX Select one: O True O False

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Q: 15. (D* – 1)y : = sin 2x

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Q: 5. y" – 4y' + 13y = 4e* sin 3x

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Q: Q.43) 2n S Icosx – sinx|dx =

A: Here we have to find solution of given integral

Q: Simplify (if necessary) then 2 Compute: y" +Éy' for a2 y(z) = rar (zx+ cosx')] [6(cosh2x- sinh2x)] d…

A: given yz=∂2∂x∂zz2x+cosx96cosh2x-6sinh2x36cos2πxddx3x2 claim- if necessary simplify then compute the…

Q: c fx) = at (4, 2) 3x – 4 d y=x In x at (0, 1) sin3x at y =- x? 4 e T 2

A: Part(c): Given function is, fx=x33x-4 at 4,2 To find the gradient of a function (which is a vector),…

Q: y" + 4y – 5y = –260 sin(5x).

A: To solve the given differential equation

Q: d²y If y=cos 2x, then at x= 0 dx? O a. 2 O b.4 O C. -4 O d.-2

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Q: 2 7 O Use the Trapezoidal rule with n= 4 to approximate the value of sin (x² )dx.

A: Given  0∫2√π sin(x2)dx  Let f(x) = sin(x2 )  Approximately the value f(x) by using trapezoidal rule…

Q: Calculate x²+y² =4 and Sin (yetp) dA,D between. ty2 = 16 abore y=0 2 %3D

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Q: Q4) A) Determine the following 1)√√²/1dx 1)ƒ cosxdx 2) S dx 2+3sinx

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Q: 4x-6z+5 2+3cosz sin z 9. Find dz.

A: Here we have to integrate the given Integral.

Q: y у +4у%3D 16t cos 2t

A: We have to solve the differential equation…

Q: Evaluate: | (cosh²2r+ sinh²2r) dr (A 2r +C 1 -sinh 2r +C 2 B -sinh 4r +C 4 D r +C E None

A: cosh²(2r)+sinh²(2r)= cosh(4r) ∫cosh(x)dx= sinh(x)+C, C is a constant.

Q: Q.2 x?dy – sin 2xdx + 3xydx 0

A: First we check type of differential equations  Separable differential equation Homogeneous…

Q: 6. y" – 4y' + 4y = 8+ sin 2t

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Q: Q1 Evaluate 2 2 || 2y? sin(ry) dydx

A: Use change of integration.

Q: Q57.a) Find if y=sin(tant) and t=cos(x) dx

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Q: i) L {8e")=? ii) L{2cos3t}=? iii) L {e²*sin4t}=?

A: Note some formula of laplace transfomation : Leat=1s-a Lcos at=ss2+a2 Leatsin bt=bs-a2+b2

Q: Q2: Evaluate ſGeascos² (y s) ds. COS

A: Using cos2(bs) = (1/2)*(1+cos(2bs) And integrating using by parts.

Q: 26. y" – 6y' + 13y = xe3* sin 2x |

A:

Q: Evaluate: (cosh²2r+ sinh²2r) dr A r +C -sinh 4r +C 4 B (c) None - sinh 2r + C 2r +C

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Q: o find for: y = sin(x") + 2* +n

A: Given,          y=sinxx+2x+π

Q: Evaluate L{3 (t² – 1) sin (2t) + 7et cosh (4t)}

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Q: Q10. If f(x, y) = cos( 3x + y) Find:

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Q: - Find y for the following: y" – 9y = 6x*e 3* – 2e-2*sin (9x)

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Q: -dnd auf for the feaoy) =tan Cx+y). 3xし y

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Q: Q12) If w=f(a,b,c)=cos(ab)sin(b)+c, what is at ( -,6 )?

A: Given ,fa,b,c=Cos abSin b+CPut 12,π3,6i.ea=12 ; b=π3 ; C=6

Q: +C 498 (9y) - sin° (9y) dy : COS

A:

Q: 2) y" + 4y + 4y = 3 sin(3r).

A: We need to solve D.E. NOTE - As per Bartleby's guidelines we can solve one question from multiple…

Q: y"+9y'=cos^2t+cosht+sinht+sin^2t+3sin-3t 7:41 PM /

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Q: Q4: Evaluate L(t cos(3t)).

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Q: y' – 2y + y = 7e" + 75 sin(2x) %3D

A: Given differential equation is…

Q: Q4/ a2w a2w Find and where w = sin(xy) cec(cos(x+y)) дх ду ду дх

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Q: (i) f(t)= est+cos 4t

A: According to company's rules, I need to solve first question when multiple questions are posted...…

Q: 3. What we want to do next is write (x + jy)as Re16 where R = J(x² + y² ) and tan-(0) = ()

A: (As per Bartle by Guidelines, we can answer only one question. Please upload the other questions…

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.