v² operates on sin(-3x) + cos(3y)

Q: y" + 3y' +2y=(− 4x² − x + 1)cos 2x − (2x² + 2x +1)sin 2x

A: To solve the differential equation of the form y''+ay'+by=A(x)cosbx+B(x)sinbx Assume the particular…

Q: 3 S² x³ cos x ²dx 6.

A:

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: (b) (cos(x) (2x + 3))'

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Q: The f sin 2x cos 2x dx is 1+3 cos 4x 1 sin²4x + C 24 1 In|1 + 3 cos 4x| + C 12 {A} {B} {C} - In|1 +…

A: To find the value of the given integral ∫sin2xcos2x1+3cos4xdx using substitution

Q: 18) e2x = sin(x + 3y)

A:

Q: 3. [(3t +r*)sin (21)dt /

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Q: 2. Solve: sin 3x dr + 2y cos 3x dy = 0

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

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Q: Obtain general solution   y¹ = cos²x cos y

A: Obtain general solution  y¹ = cos²x cos y

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

A: We will find out the required solution.

Q: The solution of sin'x + 2sinx - 3 = 0 on 0°Sx< 180° is:

A: ⇒sin2x+2sinx-3=0⇒sin2x+3sinx-sinx-3=0⇒sinx(sinx+3)-1(sinx+3)=0⇒(sinx-1)(sinx+3)=0⇒sinx-1=0  OR…

Q: The f sin x cos x dx is not equal to {A} -cos 2x + C {B} sin²x + C {C}-{cos²x + C {D} sin 2x + C

A: A detailed solution is given below

Q: The f cos 5x cos x dx is 1 {A} = sin 4x - 12 1 1 {B} sin 4x + - 8 12 cos 6x + C cos 6x + C {C} {D}…

A: Given problem:-

Q: 4. The value of fx sin(x²+3) dx Acos (x²+) + C C. cos (x²+)+C B. -cos (x²+)+C D. -cos (x²+) + C

A:

Q: 2. Vsin 3x cos 3xdx

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

Q: Find the General and Particular solution of = 8 sin 4x ; y = 6 when x = 0 %3D dx

A: Since you have asked multiple questions in a single request, we would be answering only the first…

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

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Q: V = πT -0.5x Sin 4x 4 +8x-cos2x 2 - X²-4 2²- 19.5x 1.478 -1-082

A: To determine the limit of the following equation.V=π-0.5×sin 4x4+8×-cos…

Q: 3 O f sin 2x cos 2xdx 4)

A: we use substitution method

Q: / – 9x* sin²(7y") = 9x* cos²(7y/") What is y(4) if y(0) = 8? %3D %3D

A:

Q: Find the General and Particular solution of = -8 sin 4x ; y = 6 when x = o dx

A: As there are multiple questions, first one is solved here.

Q: Evaluate D³(sinx - 4e²x) A -sin x-32e²x B -cos x-32e²x (C) с cos x-32e²x D sin x-32e²x

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Q: y = cev2z + Cze + C3 cos(v2x) + C4 sin(/2x) + Czev3z + Cge + c7 cos(/3x) + Cg sin(/3x)?

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Q: y" – 2y' – 8y = 3 cos 2x + 5 sin 2x

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

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Q: Verify y = 4 cos(2x) + 6 sin(2x) is a solution to y" = -4y.

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Q: 3. f(t) = 2e3t sin 2t 3est cos 2t %3D -

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Q: 2 cos(플x-지) =D v2 TO

A: Given trigonometric equation is:  2 cosπ2x-π=2 We have to solve for x.

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

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

A: Given that:

Q: What is if z = x'y+ sin(xy²)?

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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: x cos x² 2. X C0 dx -siny

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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 the positive solution of f = 2x – cosx

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Q: 2- Calculate y": y = 5x2 Sin (3z) - 2x Cos (5x)

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

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

Q: QIN Evaulate : f v2 + cos4t sin4t dt

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

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Q: 2 cos Vx = cos (2x-1) 0<xs1

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Q: (b) Determine J cos(x²) 2x dx by using substitution method.

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Q: 11) у%3D V1- sin 2.x y =

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Q: Find the solution of d2y/dx2+4y=sin3x+cos2x

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Q: Integrate f Osin-15x+C ○ -sin-¹5x + C 1 dx 1-25x2 - 5 H|K sin ¹5x + C cos ¹5x + C

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Q: e3x [7 sin 7x + 3 cos 7x] +C 58

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

Q: 13. y = -3 sin 2mx 15. y = -sin ix 14. y = -2 sin mx 16. y = -sin jx

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Q: n3xcsC3X)ax 3. S sin2xcsc3x+cos²xcsc3x

A: SINCE YOU HAVE ASKED MULTIPLE QUESTIONS IN SINGLE REQUEST, WE WILL BE ANSWERING ONLY THE FIRST…