Solve (D2 – 2)y =0 O a. y = cqevZx + c2e¬vZx O b.y= "(c,cos/2x+ c,sin/2x) O c.y = cqevZx+czxe¬VZx O d. y = e0x(c,cosv2x + c2sin/2x)

Q: 8. (t² + 3) cos(5t) dt

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Q: 9.lf y = sin (4x – 5), then what is y'? O A. y' = - cos (4x – 5) O B. y' = - cos (4x) O c. y' = cos…

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Q: 8. Solve the ff DE y" -9y = 0 y = c₁e³x + c₂e-3x y = c₁ cos 3x + c₂ sin 3x y = ³x (c₁ cos 3x + c₂…

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Q: Find the general solution of 2ey cos 2x dx + (ey sin 2x + 3y sec2 y2)dy = 0. a. e sin 2x +y tan y? =…

A: This question is related to differetial equations, We will solve it using given information.

Q: Consider the following IVP: y" +y' = -cos x; y(0) = a, y'(0) = b Find the general solution. A y(x) =…

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Q: 1 y = e*(C, cos2x + C2sin2x) –xe*sin2x a. 2 b. y = e*(C, cos2x + C2sin2x) +xe*sin2x 1 y = e*(C,…

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Q: If cos(4x – y) = x+y, then dx A -1 - sin(4x – y) 2+4 sin(4x-y) (B) sin(4x-y) 1 1+sin(4x-y) C) 1+4…

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Q: Obtain the general solution to the equation dy dr 2+x COS x, y(0) = 2. 5.

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Q: 4x3 — 2х2 — х+5dx А. -2 TT 3 sin t 4 dt cos²t В.

A: Evaluate the integral using the second Fundamental theorem of calculus.…

Q: 2. Vsin 3x cos 3xdx

A: Given: I=∫sin3xcos53xdx For evaluating given integral, we substitute sin3x=t…

Q: (a) If y = xV², then dy dx (b) If y = (2 + sin 3x)", then d (2 + sin 3x)" = T(2 + sin 3x)=-1(cos 3x)…

A: We have to differentiate the given functions: a If y=x2, then dydx=2x2-1 b If y=2+sin 3xπ,then…

Q: 1) If y = (x − a)√2ax - x² + a² sin−¹(*—ª),t ), then y'= 2√2ax-x² a is constant.

A: As per instructions, Here is the answer of question 1

Q: What is the particular solution of (D4 + 4D² – 1)y = 44sin3x O a. cos2x O b. sin3x O C. sin2x O d.…

A: Topic- perticular integrals of differential equations

Q: Consider - 2x 2) (² f(x, y) = e fxx + fyy = 0 cos 2y - e -2y cos 2x. Verify that

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Q: Reduce to first order and solve 1> 2xy"= 3y' Cos n ii) xy"+ 2y'+zy = 0, Y, = ニ

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Q: Solve ", = c²u«» 0sxS1, t20 subject to u (0, t) = 0, u(1, 1) =0 for all t u (x, 0) = 0, u, (x, 0) =…

A: The general solution for the homogeneous wave equation…

Q: Suppose that ye cos Bx is a solution of y-y +ay -9y =0 where a and B are real constants Then the…

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Q: Find the solution. (Dª+2D3 + 10D2)y =0. @y = c,e-+czxe¯+e"(e,cos3r +c,sin3x) y = (c,+c,)x+e*(c,cos3x…

A: To solve the given Differential equation.

Q: (D2 - 3D – 4)y = -8e'co s 2t 10 2 а. Ур e*cos2x + e*sin2x %3D 13 13 b. y, =e*cos2x + 12 e*sin2x 13…

A: The given problem is to find the particular solution for the given non homogeneous linear…

Q: 2. Use Method of Undetermined Coefficients: y" - 2y' + 5y = 4e*cos2x + n IN

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Q: y''''+8y'''+32y''+64y'+39y=e^(-2x)((4-15x)cos3x-(4+15x)sin3x) Find a particular equation for:

A: The given differential equation is: y''''+8y'''+32y''+64y'+39y=e-2x ((4-15x) cos3x-(4+15x) sin3x)…

Q: dy If y = sin(6x – 4), then dx O a. 4 cos(6x – 4) O b. -4 cos(6x – 4) 6 cos(6x – 4) O d. -6сos(6x -…

A: y= sin(6x-4)

Q: Find the general solution of y" – 3y' + 2y = cos = COS

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Q: SV1- x2 sin-1x dx

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Q: 25 a²y(cos(Tz) +2) dæ dy dz

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Q: The general solution of (D²-2D+1)y=2sin x A) y=ce*+C2xeX+sinx B) y=c1eX+C2xex+cosx y=C1eX +C,XeX…

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Q: What is the particular solution of (Dª + 4D² – 1)y = 44sin3x O a. cos3x O b. cos2x O c. sin3x O d.…

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Q: d2y/dx2 +4y=sin3x+cos2x

A: Given that:

Q: Find the general solution of the d dy 2c-2v = dx 3 sin(x/2)√ √cos³(x/2)

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Q: day Find y, of 2+ + 6y = 51 cos 3x. ... a.) y, = - cos 3x + 4 sin 3x b.) y, = cos 3x-4 sin 3x c.) y,…

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Q: (D³ – D²)y = cos2t; y a. y = C, + C,t+ Cze +cos2t-sin2t 10 20 b. y = C, + Czt + Cze-2* cos2t + 10 1…

A: We have to find the general solution of the given  differential equation D3-D2y=cos2t .

Q: Find the solution. (Dé+ 9D* +24D² + 16)y = 0. y = c,cosr +c,sinr + (c,+cx)cosr+ (cz+cx) sinx y =…

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Q: Find the particular solution : y" + y' + 4y = cos3x 3 5 3 5 (a) cos3x -; sin3x (b) Yp = cos3x -…

A: Proceed as shown below...

Q: 4 cos 2y-3 dy 2у

A: NOTE: Refresh your page if you can't see any equations. .

Q: 4. (D² – 3D+ 2) y = 14 sin 2x – 18 cos 2x -

A: From the given differential equation; D2-3D+2y=14sin2x-18cos2x So, the auxiliary equation is:…

Q: Select the general solution to the equation. y" + 16y = 0 %3D Oy= C1 cos(-4x) + c2 sin(-4x) Oy= cie…

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Q: 5 Find *: (a) y = cos(11x + 2x) dy

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Q: A particular solution of y" - 3y' – 4y = 2sinx 5 -cosx 17 a. 3 COSX - 17 5 sinx 17 b. 3 -sinx 17 C.…

A: find roots for the homogeneous system

Q: Find the solution of d2y/dx2 +4y=sin3xx+cos2x

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Q: 8 cos (2r² + 2y²) dy dr Hint You could take a cab to the pole.

A: Given the integral is ∫02∫04-x28cos2x2+2y2dydx

Q: The general solution of (D2-2D+ 1)y=2sin x A у-сје*+ с2хе* + sinx + cos х y=cqe*+c2xe* +2sinx В ©…

A: Note -  Acc. to Bartleby guidelines we are supposed to do only one question. If you want more to be…

Q: Find the general solution of: y"-3y 8e* + sin 2-

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Q: 3. Solve the DE: 1 + 2.ry? ) dx + (2ya² – cos y) dy = 0, y(1) = || - -

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Q: Find the general solution of the DE: dyldx = sin(7x) cos(5x) + cos(7x) sin(5x). O y = (-1/12)…

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Q: Find the general solution: y" + 5y' + 6y = 4e¬t cos2t + sin2t A - BI -

A: Differential equations

Q: Find a particular equation for: y(4) + 8y''' + 32y'' + 64y' + 39y = e-2x[(4 - 15x) cos 3x - (4 +…

A: The given equation can be written as, y4+8y3+32y2+64y1+39y=e-2x4-15xcos3x-4+15xsin3x it is also can…

Q: Differential Equation Activity

A: To find the general solution of the given differential equation

Q: 11. y= e4x %3D 2x 12. y= e cos 3x

A: We can solve this question using chain rule and product rule of derivative.

Q: What is the particular solution of (D4 + 4D² – 1)y= 44sin3x O a. cos2x O b. cos3x O C. sin2x

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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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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.