The roots of a d.e are -1, 2tV3i What is the solution? O a. y = e*(c, cos 3x + c2 sin 3x) + c3 cos x + C4 sin x O b. y = cqe¯X + c2e(2+v3)x + c3e(2-V3)x O c. y = c1e¯^ + C2 cos 2x + c3 sin 2x O d. y = ce-X+ c2e²+v3x + C3e2+v3x O e. none of above

Q: Find all solutions of the equation in the interval [0, 2x). V2 cos 2x = 2 3n 5n 7t O A. 4' 4 - - 4 4…

A: We have to find the solution

Q: . Use Regula-Falsi method to find solutions of x = cos x which is accurate to within 10-8 . Take x,…

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Q: What is the particular solution of the function 3e" sin 5x – cos 5x? A cos 5æ + Bsin 5x + C'e" cos…

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Q: Show that (1-)dy+(cos xsin x-sy")dr =0 is an exact equation. Hence, find its general solution. Hint:…

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Q: The integration expression + 4)cos(3ln(x) +4)dx must be transformed into using suitable choice of…

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Q: What substitution should be used to solve the integral O sin u=3x/2 sec u =2x/3 sec u =3x/2 O tan u…

A: We have to solve the integral

Q: 2. y = 3e* cos 4x + 15e* sin 4x %3D

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Q: Solve che DE'sin with Euler 2?

A: For the solution follow the next steps.

Q: What substitution should be used to solve the integral x²dx |4+9x² O sin u=3x/2 sec u =2x/3 O sec u…

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Q: „In sec²(sin2y)dy can be evaluated by writing it as sec2y A sec²(sin2y) - cos2ydy None © In…

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Q: 2 3. sin³x cos³x dx OSx Show two solutions. 0.

A: Given  The integration is I=∫0π2sin3x cos3x  dx.

Q: What substitution should be used to solve the integral x²dx 4-9x2 sinu=3x/2 O sec u =2x/3 O sec u…

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Q: Solve the given differential euation: dr/dθ+rtanθ=10cosθ. 1.r=(10θ+C)tanθ 2.r=(10θ+C)cosθ…

A: In this question we have to solve the given differential equation.

Q: Solve for QIF 4 Cas G+2 sin 2Q+3in 203D0

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Q: What substitution should be used to solve the integral S O sin u=3x/2 O sec u =2x/3 O sec u =3x/2 O…

A: Evaluate the integral by using substitution method

Q: Solve the he o-3D+4)y(x) =x cos(2x) equation y,(x)=(6x+4)sin( *+4)sin(2)-cos(23) - y,(x) =(-6x-4)…

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Q: (2.) (1-(In))^ (3.) yn + sin ()

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Q: Solve 2 cos (w) +5 cos(u) +3 = 0 for all solutions. where keZ

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Q: The auxiliary roots of the auxiliary equation associated with a certain HLDE are m=±3, ±3i, + 3i.…

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Q: S cos(3z)sin1º(3z) dz C 1 (cos (3z))10 + C 3. (sin(3z))10 + C D 1 (cos (3z))1 + C 33 (sin(3z))'l + C…

A: Topic = Integration

Q: Find the iterative scheme for the root of equation sin x-3x +1=0 by Newton-Raphson method. O a. None…

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Q: Solve for a root/roots of the functions 2. x2 – 3 sin x + 2 In(x + 1) = 3. 5 Applying both a.…

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Q: 3) Express 4sin 2x+3 cos 2x in the form of Rcos (2x-a). Hence, solve the equation | 4sin 2x+3 cos 2x…

A: The given trigonometric expression is, 4sin2x+3cos2x=5432+42sin2x+332+42cos2x=545sin2x+35cos2x⋯⋯1…

Q: Find the first approximation to the root of the equation xe" – cosx =0 using Regular-Falsi method…

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Q: 4. Solve for general solution using exact method. (sin 0 - 2rcos² 0)dr + rcos0 (2rsin 0 + 1) d0 = 0

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Q: Use undetermined coefficients to find the particular solution to y" + y' – 6y = - 2000 sin(4t) -88…

A: Let's find.

Q: (12,50 Puanlar) 3- Evaluate the integral 3x +2 dx. V5 - 22 a) – 2 arcsin V5a + 3/5- a? +C b)2…

A: Given: The integral is ∫3x+25-x2dx

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

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Q: y = 3e* cos 4x + 15e* sin 4x -X -X- %3D

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Q: capacitor is constructed with two parallel metal plates each with an area of 0.61 m2 and separated…

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Q: Find the general solution of the differantial equation given by www |y" – 4y' + 5y = 3xe* – cos2x +…

A: Given y''-4y'+5y=3xex-cos2x+x+1sin2x

Q: Solve the equation in the interval 0<0< 2r. sin (40) - sin (20) = 0 What are the solutions in the…

A: Solve the given equation

Q: The suitable substitution to evaluate sin 4(x+2) dx is None OA [1-cos8(v+2)] В. [1+ C. 2 + cos8(r…

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Q: Given: z = sin 3x cos 4y Find: z ду2 -3 cos 3x sin 4y -9 sin 3x cos 4y -12 cos 3x sin 4y -16 sin 3x…

A: Differentiate the given function partially w.r.t y keeping x as constant   ∂z∂y=sin 3x×4-sin 4y…

Q: Find , if z= cos(3x² + 7y°) O 2x sin(3a? + 7y³) sin(3x² + 7y³) -9x cos(3x2 + 7y°) -6x sin(3x? + 7y°)

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Q: 2* csch (2*) cosh(2*)-sinh(2*)

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Q: if we let u-4x- 1 for the 2 tan(4x-1)-3 cos (4r-1) dx, what will be the resulting integrand? cos…

A: The given integral is  (2tan(4x-1)-3cos2(4x-1))/cos(4x-1).

Q: 1. Integrate using an appropriate method. [2si 2 sin³(r) cos² (r)dr

A: The given integral is: I=∫2sin3xcos2xdx   As we know that; The trigonometric identity; sin2x+cos2x=1…

Q: b) Use the hyperbolic identity cosh(2x) = 2 cosh? (x)–1 to solve 4 cosh(2x)- 22 cosh(x)+19 = 0.

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Q: 11 csc²(3x) cot(3x) dx =, (Use Substitution Method) 11 11 +C 6 sin (3z) 6 11 11 +C 6 sin (3z) 6 11…

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Q: Evaluate the integral. sin (6t + 17) -dt CoS 2 (6t + 17) sin (6t + 17) dt%3D cos 2 (6t + 17)

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Q: The position of a particle moving in a straight line is given by s(t) = e-*cos(5t) for > 0, where…

A: We have to find the necessary equation that must be satisfied.

Q: Find the solution in the interval from 0 ≤ θ < 2π 2sin2 x - cosx -1 = 0

A: Given : 2sin2x - cosx - 1 = 0

Q: Substitute the expressions for u and v in the integral. (글sin(| ») - / ÷a x cos 7x dx = sin( |x) dx…

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Q: 4. Solve for all solutions to sin 3xcos 2x + cos 3x sin 2x =1 on [0, 2

A: Given: sin3xcos2x+cos3xsin2x=1 Identity Used: sinacosb+cosasinb=sina+b

Q: find the roots of the equation x*cos(x) = -1 In[-2,4] using bisection method with error = or less…

A: For the solution of the problem follow the next step.

Q: The solution of some second order linear DEQ is exp(-7x)[5sin(1x)+ 7cos(1x)] which can also be…

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Q: b) Is S cos4xV2 – sin4x dx (2 – sin4x)³ + C true or false? show me

A: this is false because

Q: 2. Find the solution set on [0, 2n). sin²(x) + cos² (;) – : -2 =0

A: