Solve the following second-order differential equation: yn+ 4y'+ 5y = 8x sin x

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A: here we have to find characteristic equation and solutions of given differential equation.

Q: Consider the following differential equation. y"-y'-30y 0 Verify that the functions .-5x and 6x form...

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Q: determine the most general function M(x, y) or N(x, y) so that equation is exact.

A: We have to find M(x, y) Or N(x, y). 

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A: Stoke's Theorem : ∮F→.dr→ = ∫∫ F→.n^ dS

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A: Position function of a particle is given by r→t=t2,5t,t2-16t for t≥0 We have to find the time and po...

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A: Let us solve the problem using the basic equation of ellipse  later we will use different methods to...

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A: Solution ) A function f(x,y) is homogenous of degree 7 in x and y if and only if f (kx , ky ) =k7f(x...

Q: Find

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Q: dx 4. Evaluate the integral by trigonometric substitution: , Væ²-9

A: We can find the integral using trigonometric substitution as below

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Q: [4x°cos(xy)-x*ysin(xy)– ye" +3x³]dx -[x°sin(xy)+ xe" +6y°]dy = 0

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Q: Use the Integral Test to determine whether the infinite series is convergent. -n2 16пе n=6 Fill in t...

A: This is a question related to series and sequence calculation. For using integral test for given ser...

Q: 4. Find the equation of the plane that passes through the point (5, –1,0), and is pendicular to the ...

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Q: Determine the derivative of f(x) = 3 x² In x with respect to x. f'(x) = |

A: We have to find f'(x)

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A: Given:   limx→0+x14 ecosπ18x

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A: Given that: ydx=x+y2-x2dy

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Q: S 4- e-2) cos(e- + In z) dz

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A: Given that 2x2+y22=25x2-y2To find : equation of tangent line at point 3,1Solution :2x2+y22=25x2-y22×...

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A: We need to find equation of line.

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A: Given: y=Ce-mx

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A: Area of parallelogram of the vectors a and b is a×b.

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Q: Which of the following is not true? (A) - |f(x) dx- J8 (x) dx B) 8 (x) dx C) (x)dx=k (D) O fas(3))dx...

A: some properties of the integration are given, we have to find the not true statement.

Q: 2e*dx where e = 2.7183 %3D

A: Given: I=∫012exdx   As we know from the integral; ∫a·fxdx=a·∫fxdx, where 'a' is the constant. And ∫e...

Q: dy 9x using 5. Find the slope field of dx GeoGebra.

A: This is a problem of the slope filed plotting. In this given question dy/dx is representing slope of...

Q: The function in the figure below has f(4) 21 and f' (4) = 1.8. Find the coordinates of the points A,...

A: Given that: f(4)=21, f'(4)=1.8

Q: Use the Integral Test to determine whether the infinite series is convergent. n=1 Fill in the corres...

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Q: on - Homogenous: To be considered Homogenous, the differential equation must be equal to ependent va...

A: We are asked to find the  non homogeneous second order euqation.

Q: Find the area between the curve and the x-axis for the function y = x2 +3x between x= -1 and x = 2 a...

A: To

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Q: Find the volume of the solid obtained by rotating the region bounded by y = x – x^2 and y=0 about th...

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Q: 1 (i) lim 3n2 – 4000 のlim(- 2n2 +10000 X00

A: Topic:- calculus

Q: 2. lim f(x) and lim f(x) if f(x) = V4-x2 %3D X-2+ X→2- х-2

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Q: 1 I. Evaluate dV, where E lies between the spheres x? + y² + z² = 1 and x2 + y? + z² E x2 + y? + z? ...

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Q: nd [(dy)/(dx)] if the curve is defined by 7 x? e7y + 6 y² e² x

A: We are asked to find the derivative 

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A: Topic:- application of integration

Q: Please solve and show all work. Thank you!

A: Topic:- geometry

Q: (a) y = -T (b) y = 2x° + 3x (c) y = x² + 5x 7 (d) y = x(x - 1) %3D -

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Q: 3.b) Evaluate the DE * 3x(xy – 2) dx + (x³ + 2y)dy = 0

A: Given that: 3x(xy-2)dx+(x3+2y)dy=0

Q: [5tan 20 elan 28 sec? 2 Bd B 1.

A: Gievn, ∫5tan2βetan2βsec22β dβ We can solve this by substituting u=tan2β