9. What is the general solution for the differential equation y"" - 3y' - 2y = 3x? A. y C₁x + C₂xe-x+cos x - sin x 3 9 B. y = C₁e-2x - C₂ex + ₂xe¯x + ²x -x- 4 C. y = C₁x + C₂e-x - cos x -sin x + 4xe-x 9 D. y = C₁e²x + C₂e-x + 3xe-x-²x + 4 10. What is the general solution for the differential equation dsy d³y dx5 +4 = 72 dx3 A. y = C₁ + C₂x + C3x² + C4 cos 2x + C5 sin 2x B. y C₁e + C₂x + C3x² + C4 cos x - C5 sin x C. y = Cx + Cze-* — cos x − ,sin x + 4xe-x 1 2 D. y = C₁e²x + C₂e-x + C3xe-x-sin x + cos2x

Q: Solve the integral: A B с 1 √√x+x √√ Sin/1+x²|+c -In +C 6in|5+ x²|+C с {in/1+x³ |+c C dx

A:

Q: Determine the integral: x²cosxdx A x²sinx+2xcosx + 2 sinx + C B x²sinx-2xcosx-2sinx + C C)…

A:

Q: A freshly brewed cup of coffee has temperature 95°C in a 20°C room. When its temperature is 73°C, it…

A:

Q: At what points does the helix r(t) = (sin(t), cos(t), t) intersect the sphere x² + y² + z² = 82?…

A: This question can be solved by putting x=sint, y=cost, z=t in the equation of sphere to obtain the…

Q: A 6-ft man walks away from a 16-ft high lamp post at the rate of 4 ft/s.  How fast does the tip of…

A: Given that, A 6-ft man walks away from a 16-ft high lamp post at the rate of 4 ft/s.

Q: Find the absolute maximum and minimum values of the function, subject to the given constraints.…

A:

Q: y" - 3y' + 2y = 2x² + ex + 2xe* +4e³x

A: As per the company's guidelines we are supposed to solve first question for you, kindly repost other…

Q: Find L-1 ((₁+1)² (s+1)(s²-1)/

A:

Q: Solve the following. Choose five In(x+2) dx 1. S 2x+4 2. fx² ex dx 3. f tan³x dx 12 dx 1+9x² x-2 5.…

A: As per our guideline if multiple questions are posted we are supposed to answer only the first one…

Q: 1. f In(x+2) dx 2x+4 2. fx² ex dx 3. f tan³x dx 12

A: We know that integration of xn is xn+1 /n+1. And integration of 1/x is lnx +c.   Here i attached the…

Q: y = 3Arcsin (2x³) -- Arccos(2x³)

A:

Q: A 5kg sample of plutonium-239 has a half-life of 21,400 years by emitting a 5.157 MeV (million or…

A: Let's find time to taken sample to degrade to 4.5kg.

Q: y'+xy=xy^3 Solve for the solution What is the integrating factor? What is the dependent variable?

A:

Q: d²y If x=5+ cos20 and y=3- sin20, what is ? dx² A csc ³20 (в B - cot20 Ⓒ-csc ³20 D cot20

A: Given: x=5+cos2θ and y=3-sin2θ Now, dxdθ=d5+cos2θdθ=-2sin2θ and    dydθ=d3-sin2θdθ=-2cos2θ Now…

Q: In (x-2) lim x2+ In (x² −4)

A:

Q: Determine the area bounded by f(x)=x²-x and x-axis. Ⓒ / unit² A ® B / unit² © unit² D -unit²

A:

Q: 3. Look at the figure below. Find the value of x and the measure of each angle. n 1.x = 2.42 = 3.26…

A: We know that alternative interior angles are same Therefore 5x-14=3x+18 Subtract 3x+18 from both…

Q: + 1) dx A B C (x + 2) (x - 1)² = √ [++^2 + == 1 + (0-12 dc. ]dx. dx, the values of A & C…

A:

Q: Which of the following represents the volume of the solid generated by revolving the region bounded…

A:

Q: (a) dy Given 4 sin 3x + 2exy = (2x + y)³, find dx'

A:

Q: 2. fx²ex dx

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

Q: If given integrand is x² cos 2x dx and dv is equal to cos 2x dx, what is v?

A:

Q: Solve the following y" - 3y' + 2y = 2x2 + ex + 2xex + 4e3x -

A:

Q: 3 [²(x²) dx 0 Using the definition of definite integral, ff(x)dx= lim f(x) Ax, and the given…

A: Given, ∫03x2dx

Q: Stretching spring: Eighteen pounds of force is required to stretch a spring 3 ft. from its natural…

A:

Q: (D) 1

A:

Q: sinh x tex + ex cosh x In the indefinite Integral in(cosh x + ex)- sinh x tex A In(cosh x + e*)-…

A: Answer: A

Q: Determine the area bounded by the functions f(x) = (x + 1)³ and g(x)=x+1₁ 3 A unit² ℗ 1/2 B D unit²…

A:

Q: Find the length of the curve of 8x = y² + 2y-² from y = 1 to y = 2.

A: Length

Q: The hyperbolic paraboloid (saddle) f(x, y) = x² - y² + 4 is shown in the 3D model below. Find the…

A: Here, to find the volume f(x,y)=x2-y2+4 between the rectangle R=[-2,4]×[-1,2]

Q: . The Minimum point of y = x3 3x+6

A:

Q: 6. Find the area enclosed by the curve x² + 8y + 16 = 0 the x-axis, the y- axis and the x-4 = 0…

A:

Q: 12. Find the first and second derivatives of f (x) at x = 1.2 and x=2.0 from the following table 1.2…

A:

Q: Which of the following represents the volume of the solid generated by revolving the region bounded…

A:

Q: Evaluate the triple integral: A) 12 B) 24 C) 6 D) 18 3 2 (x+y+z)dydxdz

A: To evaluate the given triple integral.

Q: A tank contains 50-liters of brine in which 20 grams of salt is dissolved. Pure water is being…

A:

Q: Given f(x)=4x+1 and g(x)= x²+x-3: Use the washer method to determine the volume of solid obtained by…

A: Let's find volume of solid by using washer method when given two curves rotated about x axis.

Q: dx Transforming secx + 1 2-2z² A 1+z² ® √ ₁ + 2²/1d² +z² B -dz 1-z² z²+z C / 1-z² Ⓒ / 1-²/²0 D 1+z²…

A: To find the transformation of the integral ∫dxsec x+1 after using miscellaneous substitution.

Q: Find the volume of solid generated by revolving the region bounded by f(x) = x² + 1and g(x) =…

A: Given that , fx=x2+1 and gx=-x2+2x+5 find the volume of solid generated by revolving the region…

Q: O O O O It is reflected over the x-axis and shifted right three units. It is reflected over the…

A:

Q: To reduce the DE (x+2y-4)dx-(2x+y-5)dy=0 to a DE with homogeneous coefficients, use the…

A: solution:-x+2y-4dx-2x+y-5dy=0dydx=x+2y-42x+y-5the system of linear equation…

Q: What is the annihilator for y=x e*cos 2x ?

A: Our Aim is to compute the annihilator for y=x ex cos 2x -(i)

Q: Evaluate each of the following line integrals. Jc [(3x² - 3yz + 2xz)dx + (3y² - 3xz + z²)dy+ (3z² −…

A: Solved below.

Q: z = xey + yex, Find əz əz дх'ду

A: Given: z=xey+yex To find : ∂z∂x,∂z∂y For ∂z∂x, we have to do the partial differentiation of z with…

Q: the equation of the tangent line to the curve y = 4 sin x at the point equation of this tangent line…

A: We are asked to find the tangent line of the curve.

Q: Find the volume of solid generated by revolving the region bounded by f(x)= x² + 1and g(x) =…

A:

Q: Which of the following is homogenous of smallest degree? (A) In x - In y B x+y x-y C √x-y x² + y4 X…

A:

Q: Solve the integral: Seln(2x² + 3x-4)³ (4x + 3)dx A eln(2x² + 3x-4)³ (4x+3) 3(2x²+3x-4) (2x²+3x+4)4 B…

A:

Q: 7.Find of z = x3 + 5x2 y + 6 02z дхду

A: find ∂2z∂x∂y of z=x3+5x2y+6 formula: ∂xn∂x=nxn-1

Q: Find the area bounded by : f(x)=e*, g(x)=e* and x=3. A (e²-1)² e2 sq. units (e³ + 1)² e3 (e²+ 1)² e²…

A: Given:-the region bounded byf(x)=ex, g(x)=e-xand x=3