O y = C1e- Solve 2 y" +2 y' + 3 y = 0 O y = C1e¯i" cos(x) + C2 e ¯ sin(æ) COS C;e * cos(=) + C2 e sin(=) V5 CoS V5 /5 Oy = Cje= cos(a) + C2 e- sin 2 O y = C1e-# cos(x) + C2 e-® sin(x) CoS

Q: 9 NO ION If g(x) = [ cos t dt, find g '(x). %3D x10 -sin (x) -10x cos (x) COS 1 cos (x°) %3 10x9 cos…

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Q: B.S(cos x + cos 5x)dx D.S(cos x – cos 5x)dx A.S(sin x + sin 5x)dx C.S(sin x – sin 5x)dx 8. S sec³x…

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Q: 3. Verify that ysin x-xy =0 is a solution of the equation y(cosx-y)dr+(sin x- 2xy)dy =0.

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Q: 11, 0-20² 2. 3. चं 5. T S cos 2x dx sin(²³) cos²(:-) / dx 2x-1 4x dx dx 6. 7. 8. S [² (x² + 0²³) dx…

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

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Q: f(x)=X +Sin -1 く(-2)- 4-て+Sini-て)-\no9651 3(x)=てメ+ cosx ずし-て) ニ -4ACOS(-て)-3 (x)-2-らinx f(-2):…

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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: y = In(cos 3x) %3D 1 (- sin 3x)(3) Cos 3x y' %3D y' = 1 (- sin 3x) cos 3x 1 y' = (3) sin 3x %3D -…

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Q: If y = sin(x + 4) cos(7 – x), then is dx A. sin(2r – 3) B. -sin(7–x) cos(x+4) C. cos(2r – 3) D.…

A: We have to find derivative

Q: Q#( 1b Compute: [cos (10x)sin²(10x)dx 1 sin°(10x) – A) 30 1 sin°(10x)+C 50 1 cos°(10x)- 1 -cos…

A: We have to solve the given indefinite integral

Q: 1. * Sx² sin 2x dx -x²cos2x ¸ x sin 2x , cos 2x +C 8. –x²cos2x x sin 2x , cos 2x + C A 2 2 B…

A: To Find : ∫x2sin(2x)dx

Q: What is the general solution to the differential equation sin y (x + sin y)dx + 2x² cos y dy = 0 ?…

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Q: 3+2cosx dx is equal to (2+3cosx) sin x 2 cosx 2+3cos x) 2+3sin x 2 cos x 2 sin x (d) 2+3cosx 2+3sin…

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Q: 3- The integration of ſ cos(7x + 5).dx is: (a) cos(7x + 5) + C (b) sin(7x + 5) + C (e)극 sin(7x + 5)…

A: The given integral is, I=∫cos7x+5dx Now, substitute z=7x+5in the above integral,…

Q: [ 2x sin (4x)dx O =cos (4x) + C -x² 4 2 sin (4x) + 8x cos (4x) + C sin (4x) – x cos (4x) + C ○중cos…

A: Integration by parts

Q: 1. If x - y = 25, then y" = c.) d.) - a.) b.) 2. If y = cos(3x+1), find y a.) 3 sin(3x+1) b.) -3…

A: Authoring guideline: As per the authoring guidelines, we can solve only the first three parts.…

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

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Q: Give the general solution of the differential equation p"+ 25 y =2 sec( 5 x) a) O y=C, sin(5 x) + C,…

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

Q: 21. If y=(x* +sin x)", then dy dx (A) 6(x*+sinx) (4x-cos.x) (B) 6(x*+sinx) (4x' +cosx) (C)…

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Q: Find the general solution to 2- ди u = xt + x cos t + t sin x. 3 - -

A: Given: 2∂u∂t-3∂u∂x-u=xt+x cos t+t sin x

Q: 24. Evaluate: S(cos 2x) esin 2x dx A. -e sinzx + C esinzx +C C. esinzx + C esinzx D. + C В.…

A: using substitution method to solve integration

Q: 11 Evaluate || sin(y)dydx where 2: 0<y<1, 0<x<y. 0 x a) 1-cos(x) 1 b) (1–cos(x)) e) ,-cos(1) d) 1…

A: This integral can be solved by changing the order of the integral. The order can be changed by…

Q: Differentiate: y = In cosh (cos 2) O y' = 6 sin 2z tanh(cos 2z) y' = -6 sin 2a coth(cos 2x) Oy = -6…

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Q: Find the solution of these differential equations : 1. dx %3D ху — у sin x dy 2. 1+v dx = cos x cOS…

A: Given that  The following differential equations  To find out the solution of the differential…

Q: Show that an implicit solution of 2x sin?(y) dx – (x² + 17) cos(y) dy = 0 is given by In(x2 + 17) +…

A: To find- Show that an implicit solution of 2x sin2y dx - x2 + 17 cosy dy = 0 is given by lnx2 + 17 +…

Q: f(x)=X +Sin -1 く(-2)- 4-て+Sini-て)-\no9651 3(x)=てメ+ cosx ずし-て) ニ -4ACOS(-て)-3 (x)-2-らinx f(-2):…

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Q: Integrate with respect to x: sin(3x) a b 2 cos(4x) cos (2r) (5) f e2x cos² () d 3 cos 3 sin(2a) — е…

A: We have to solve the following integral .

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: The general solution of y" + 16y3 cost is: Select one: a. y= C, cos(4t) + C2 sin(4t) + 1 -tcost 15 O…

A: Using Solution of Linear Differential Equation

Q: Solve the exact differential equation (In y - y sin x-6e)dx+(÷- + cos x + 5 sec y tan y -6y)dy = 0 A…

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Q: sin COS dx V 32 COS 35 5cos² + C O 32 COS 32 + 4 COS 4 口 32 cosS Ssin+2-c cos () + c 35 4 4 32 CoS 7…

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Q: $5. (i) show that: sin 0+sin 20 = tan 0 1+cos 0+cos 20 (ii)Find the general solution of the equation…

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Q: z sin(2- 32)+cos(2 - 3a)+c | 4x cos(2 – 3x) dx 4x cos(3 3r) dx Option 1 Option 2 |4 cos(3- 3z) dr…

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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: 35. Given that d = 6(sin 2x - cos 3x) and y = 0 dx when x = 0, y = A -3 cos 2x - 2 sin 3x – 3 B 3…

A: We can solve this problem using initial value problem.

Q: Find y, of 2 -3+2y 6 cos x+9 sin x dx ... a.) y, = 3 cos x+ 2 sin x b.) y, = 3 coS x- 2 sin x c.) y,…

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Q: Integrate with respect to x: sin(3r) a b 2 cos(4x) cos (2r) (5) f e2x cos² () d 3 cos 3 sin(2a) — е…

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Q: (1) ſ [ (x³ + 2 + 7 ) dx (3) cos³x dx (2) √ x³ (2) x3 e3x+1 dx (4) sin x sin 2x dx

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Q: 6. S cos 4x cosx dx will yield B.금sin Sx + 등sin 3x +c А. sin 5x + sin 3x + C c. 글cos 5x-글cos 3x + C…

A: Note: As per company policy we should solve only one question. So kindly repost the other questions…

Q: Differentiate y= e*cos (x2): y' = A -e*sin(x²) e(cos(x²) – 2 xsin(x²)) e*cos(x?) – 2 xsin(x²) D -2…

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Q: Find the particular solution using the initial condition. y' sin(2y) - cos x = 0, y() = 0 O y = cos…

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Q: Solve the initial value DE y - ytanz = sinx, y(o) = 1 5-Cos 2x 5-Cos 3x 5-Cos 2x Cos 2x A) y = B) y…

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Q: Obtain the solution to the differential equation: (cos'x- cos'y ]dx+ cosx sin 2ydy = 0 a. cos"y(1+…

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Q: Show that an implicit solution of 2x sin?(y) dx - (x2 + 17) cos(y) dy = 0 is given by In(x? + 17) +…

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Q: Solve the initial value problem y′′ + 9y = cos(3x)+sin(3x) for y(0)= 2, y′(0)= 1.

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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: Determine the general solution of (cos(x)cos(y)-cot(x))dx=(sin(x)sin(y))dy

A: Given: cos(x)cos(y)-cot(x)dx=sin(x)sin(y)dy

Q: 16. √(16-9x²) dx 17. dx/ (9x² + 4) 18. sin³ x cos x dx 19. f (secs x) dx/csc x 20. Stan² x dx

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