1 (ysin x + y?) dх — + cosx – 2xy) dy = 0 - \y²+1

Q: Z and dy 없 of y%3 (5x2 - ) (cos ar d²y Determine (cos x + In x).

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Q: Evaluate (x²sin y-xcos(y)) dy A x²(1+ sin(1))-xcos (1) + C B x²(1-cos(1))-xsin (1) + C C 2sin…

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Q: Find the particular solution : y" + y' + 16y = sin4x 1 (а) Ур — — 4sin4x (b) Ур 3sin4x --cos4x 1 (c)…

A: Correct option: C The detailed answer is listed below, kindly do like it if you find my answer is…

Q: 4sin 5x cos 3x-4cos 5x sin 3x/rom x= 0 to x= 2m

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Q: 2 sin? 11. y = 3x 2x2 12. y = cos°V2x – 1 3. 13. у %3D Vtan(х?)

A: As we know that; The chain rule: fgx'=f'gx·g'x The Quotient rule: fg'=f'·g-g'·fg2 The Power rule:…

Q: ) Evaluate A) /16 /2 cos (167 x5 ) dx dy. Os xs 2 Og y s x*

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Q: 5. S 11 sin ( 4x – 6y) cos ( 6x – 4y) dy - -

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Q: find the volume of the solid

A: Find volume of solid.Sketch the given function.

Q: nx and y=cosx from x=- to x=- 4 4

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Q: 1 1 S [ sin(1+ y²)dydx= 1- cosl a. 2 cos 5

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Q: 4. Find fyryzyaz, if f(r, y) = x² cos[100(e" + /1+ y²)®]

A: Given; f(x,y) = x2cos[100(ey+√(1+y2))y]

Q: 5 Evaluate the integral 2x cos(xy)dydx 4 0.

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Q: y 2sin x-cos 2.x for 0° sxs360

A: Consider the function, y=2sinx-cos2x Differentiate with respect of x,…

Q: 1. If f(x, y)=3x' sin y- y² cos x- 2yln x– xh y- 4xy , find- of ôf ô²ƒ ô²ƒ

A: Given: fx,y=3x3siny-y2cosx-2ylnx-xlny-4xy2

Q: 1. If y=tanx, prove that y=2(y² +1)(3y² +1).

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Q: π/2 1-z [²6² x cos ydzdydx = = [Show your solution.]

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Q: 1) x² sin(y') + xe2 – cos(z?) = 3y– 6z + 8 cos(z?) = 3y – 6z + 8 %3D -

A: Given; x2siny3+xe3z-cosz2=3y-6z+8 Now differentiate partially with respect to x we get,…

Q: 7 xsiny dx + Cx²+1)cosy dy = 0, yC)=TT/2

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Q: 22 3x'y = 2ty- 3). 23 (2y cos x + sin* x) dx sin x dy; when x Ans. y= cty- 3) exp (x n, y = 1. %3D…

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Q: 3. = Cos xsin +xax+a 5/2 3/2 1. Ans: Y= 4sin'x* sinx+ To CAx+4)^- Cax+a) 3.

A: To solve: dydx=cos3x sin2x+x2x+1 Solution Given differential equation can be written as: dy=cos3x…

Q: 3) = + sin (4) r = y(In y- In r+1)

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Q: azz = e2x-y + cos(-3x + 2y) + 3x, дхду Given that az where əx 5x2 – sin (3x) when y = 0, and Z =…

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Q: S2ta J 2tan x In (cos x) dx=

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Q: 3e'x In cos2x Vxy = 1 y? x+1 7 In (xy)-3sin 2y |- 2y = 0

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Q: 10. Given that 2y- sin 2x =0 and y = 0 when x 0, then y?= %3D %3D dx B. 1-cos 2x C.-2 cos 2x A.…

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Q: hD (Hint: E =eD and Sinh x: 2 Q3: Prove that 8 = 2Sinh %3D

A: We will prove the following result.

Q: 7 Integrate by using the Archimedes-Riemann Theorem | (2.02 + x)dx

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Q: I need solution to this problem.

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Q: i. Jsin xcos 2x - sin 2x cos xdx

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Q: D. 1. If (x + y)² = x² + y² 2. If y = sin³ () cos³ () dy - dx X prove that y' = sin² (x) cos(x) 8…

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Q: 18) * x-sin 2x ; find y" y y" cos 2x y = 7 %3D Option 3 O Option 1 y" sin 2x

A: First we find out first derivative with respect to x then we find out 2nd derivative with respect to…

Q: 3Tt of cSC X du If u = f(x), then dx cos X . Compute %3D 2 sin x и -

A: Given ,  u = f(x)

Q: 2 Find the general Solution of yty = 2xcosx -CosX %3D

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Q: Verify that y = 7 sin 2x + 9 cos 2x is a solution of y" + 4y = 0 %3D

A: Given, y = 7sin2x +9cos2x  We have to verify y = 7sin2x +9cos2x is a solution of y"+4y = 0

Q: find do diy y = (cos(x))*os)

A: Given y=(cos(x))^(cosx) Now differentiate y with respect to x

Q: 2. y= 4sin(2x- T) and y= cos(3x-) 2

A: According to question given that y=4sin2x-πy=cos3x-π2

Q: 4. tanx dy + y3 sin? x dx %3D 0, whe х %3D0, у%3D 1 о у?(3- сos 2x) %3D2 о у (сos 2x - 2x) %3D 1 о…

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Q: 1. If y= tanx, prove that y"=2(y² +1)(3y² +1).

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Q: 3. f(x,y)= In(x cos y)-cos (In3y)+

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Q: 7. Over the domain 0s x s2n, the equation cos(x)-sin(x)%3D2 cos(2x) has:

A: We find the solution in the following way by using trig identities.

Q: 1- LS7 cos(y)esin(y)+9x dydx 2

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Q: 1. Find Duf at P: f(x,y) = sin(8x – 5y); P (5,8)); u = (i-)

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Q: A particular solution for y +2y +y=1-cosX

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Q: 4. y"+ 25y = 0; yi = cos 5x, y2 = sin 5x; y(0): y'(0) = -10 %3D %3D %3D 2x. u0)

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Q: 1. y = Arctan 3-V9-x2 2. y = 4 Arccos + 2v4 - x2 2 y = In (*+2), (x-1)2 3. у%3DIn

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Q: 3) e4x = sin(3x + 4y)

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Q: 0.5 COS T - In(4 sin z) dz. J0.1

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Q: (2e" sin(y) – 4y)dr + (–7x - e cos(3)dy = 0 not exact

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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.