dv +w + v = 5 In solving differen tial equation system dx v(x) =? dw dv 9v = 10e*, dx dx A) v(x) = c,cos3x + c2 sin3x – e* B) v(x) = c, cos2x + c,sin2x + e² C) v(x) = c,cos2x + c2sin2x +e²x D) v(x) = c,cos3x + czsin3x + e* E) v(x) = c,cosx +c2sinx + e*

Q: / (csc 2x)(cot 2x cos 2x + cot 2x cos 2x) dx

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Q: 1 Evalute: dx (x'+2x+2)'

A: Please refer the attached image for complete solution.

Q: (D-00-60)2 (2x +) COS

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Q: 2x+5 dx = AV7- 6x - x2 + B sin - (**)- 1. Vア-6xーx2 +C

A: ∫2x+57-6x-x2

Q: sinx

A:

Q: Find the general solution of the D.E. ye? dx = (4+e2") dy Show your solutions on a separate sheet of…

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Q: sin(7x 2) dx cos2 (7x 2)

A: Let u=cos(7x+2)differentiate both sides w.r.t. x.Use chain rule for cos(7x+2)From there we get du/-7…

Q: 1) - 3dx 2) (2-3x)² dx 3) x sin (2x2 - 1) dx (2x-3)2 4) sin3x cos² 3x dx

A: Step 1:Step 2: Step 3: Step 4:

Q: Solve the equation (y - (cos x)^2)dx + (cos x) dy = 0

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Q: cscx−sinx cos²x CSC X =

A: We need to prove that cscx-sinxcscx=cos2x

Q: Find the solution. (403+12D²+13D+10)y = 0. @ y=c,e+e>(c,cosx + c sinx) +c,sinx) -3x y =…

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Q: t 3X +5) C

A: on doing integration we get

Q: / (cos(x) + Ex dx 4 +

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Q: Ssin8 (3z) cos5 (3z) dz

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Q: (5x+sin3(4x) + sin(4x³)) dx

A: use differentiation for finding the solution.

Q: $66)=Sinx+ Cosx %D

A: “Since you have asked multiple question, we will solve the first question for you. If youwant any…

Q: 4. tan²B + 1 = sec² B

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Q: cos^2(3x)+4cos(3x)=5   give all solutions such that x [0degrees,360degrees]

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Q: sin(2x) dx cos(2x)+5 2x dx V3x +1 4 sec2(2x) dx ! 3(1-tan 2x)

A:

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.