Determine c1 and c2 so that y(x) = c1 sin 2x + c2 cos 2x + 1 will satisfy the conditions y (π/8) = 0 and y′ (π/8) = √2

Q: ду Let y = In Vx² + 2z3 + cos(b³), find

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Q: -) Find the general solution of the DE y(4) + 2y" + y = 3 sin t - 5 cos t Use the method of…

A: We can solve this ordinary differential equation by undetermined coefficient

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Q: Is the ODE (sin(x-y)+1)dx=(sin(x-y)-2y)dy satisfied by the implicit solution x+y2=cos(x-y). Show…

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Q: 3. Find dy, where; a) cos(ry) - e 2 elx+y). b) ė?+ Ptany =4, u= xlax (use chain rule)

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Q: 7. Differentiate w.r.t x- sin 5x cos 3x

A: Given problem:- Differentiate w.r.t  x sin5xcos3x

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

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Q: This is the solution of the Cauchy - Euler equation xy" + 5xy' + 20y = 0 %3D O y = C1x4 cos(4 ln(x))…

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Q: (cos 2y – 3x²y²)dx + (cos 2y – 2x sin 2y – 2x³y)dy = 0 |

A: We will find out the required solution.

Q: 1. Determine the general solution of this equation in terms of C ( sin y- ysin x) dx + (cos x + x…

A: We have the following solution for given ODE:

Q: Differentiate with respect to x: y= In(3x2)/x3  and y=x2sinx/cos2x

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Q: d²y Find the solution for cos(x) (1+ x²) – 2xy = with the conditions %3D dx2 1+x2 y(1) = -1, y(2) =…

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Q: Suppose that x2y" + axy' + by = 0 has the general solution of the following form: y = x-(C, cos (3…

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Q: determine the annihilator of the givenfunction. F(x) = sin x cos3 x.

A: We have to determine the annihilator of the function: Fx=sinxcos3x Annihilator is the set of linear…

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

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Q: Q1: Use the Improved Euler method to find y' = cos2x + sin3x ,0<x < 1,y(0) = 1, with h = 0.25. %3D…

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

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Q: Verify that the indicătéd function is an exp for each solution. y" - 6y' + 25y = 0; y = e3x cos 4x…

A: Recall: (uv)'=u'v+uv' where u and v are the function of x

Q: 2. Differentiate y os=1(-2x³ – 3)³ = cOs

A: From the given problem:   y=cos-1-2x3-33   As we know that:   cos-1x=-11-x2   So,…

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

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Q: Differentiate y= cos y2x +1 sin 2x+1 A. V2x+1 sin 2x+1 B. V2x+1 sin 2x+1 C. V2x-1 sin 2x-1 D. V2x+1

A: Please refer the attached image for complete solution. THANK YOU.

Q: Find the solution for cos(x)" - (1 + x²) – 2xy = with the conditions dx2 1+x2 y(1) = -1, y(2) = 2…

A: Given equation is  cos(x)d2ydx2-(1+x2)dydx-2xy=11+x2 with y(1)=-1 and y(2) = 2 h = 0.25 To solve  -…

Q: Q2 Q2/If y = (x³ + 5x² + 1)3 + Jsin+/cos³Vtan3x2 find y'

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Q: 2. If y = C₁ cos2x+C₂ sin 2x+2sin x is the general solution of a certain nonhomogeneous LDE, which…

A: The given general solution of non-homogeenous  LDE.  y= c1cos2x +c2sin2x +2sinx   We have to find…

Q: 2 2メ Q1 find dy for y = Cos ( In x + e

A: we have to derivative with respect to x

Q: Find the general solution using reduction of order. 1. y''+y'=cos(4x)

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Q: 1. Solve the DE: (cos y- cos x)y' +cos y sin 2x = 0

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Q: 11. Find the general solution of uyy - 4xu, = cos 2y – 2x sin 2y + 4x.

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

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Q: Obtain the General Solution of: (z + 2)* cos yudz - [sin y In(3z 4 6) – d

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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: he Solve the y)-Sy'(x)+8y(x)-4y(x)-xcos(x) equation y,0)-cos(x)+xsin(x)- 41 19 sin(x)+ cos(x)…

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Q: Find one particular solution to the following second-order forced equation d²y + 2y = cos (√2t) dt²…

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Q: find a linear homogenous constant coefficient equation with the given solution: y(x) =…

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Q: (b) Find the solution for cos(x)- (1+x?) – 2xy = with the conditions 1+x2 y(1) = -1, y(2) = 2 and h…

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Q: y" + 3y' + 2y = e* (t2 + 1) sin(2x) + 3e- cos x + 4e"

A: Answer

Q: Show that y1(t) = cos(3t) and y2(t) = sin(3t) are linearly independent for all t

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Q: Find the general solution to the DE using the method of Undetermined Coefficients: y" + 9y = 2…

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Q: 1. Find for the following functions : dx 4i) y-bmcx* +2y}kos x (ans.: 4x.cos x - 2 In( x² + 2 )sin x…

A: To find the dy/dx of  y=[ln(x²+2)²]cosx

Q: 7 (a² +b°) 1 Prove that : dx = ở (a sin x+ b° cos² x)' 4a’b?

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

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

Q: y" + 3y' + 2y = cos4x %3D

A: Thanks for the question :)And your upvote will be really appreciable ;)

Q: find a particular solution of y"-9y=-6 cos3x *

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Q: (b) Prove that 2 -3/2 Js12 (x)dx = sin xy + C. 'COS X x2 x3

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Q: 3. Given that 2 = 6²¹ sin (u + ), e2v Use chain rule to find az/0x when x = 0, y = 0. u=e¹ - sin (y…

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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: Determine cı and c2 so that y(x) = c1 sin 2x + c2 cos 2x + 1 will satisfy the conditions y () = 0…

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Q: 44. First verify by substitution that y (x) =x=1/2 cosx is one solution (for x > 0) of Bessel's…

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Q: Find the general solution of the following first-order ODE xy' = y + 2x' sin² (2)

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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.