ーX 1- y² e*ydydx

Q: lim In(12x + 1) csc(4x) A) 0. B) 1. C) e. D) 3.

A: Given that limx→0+ ln12x+1 csc4x Evaluate the given limit

Q: 10 (3-t)√t dt

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Q: SVA 1. dt 1

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Q: 3. Scse*x dx

A: The objective of the question is evaluate the indefinite integral.

Q: 00 e-2y dy 0.

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Q: dx + 3x = e dt -2t

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Q: d²x 4. + xe0.01x = 0. JP x(0) = 1, x'(0) = 1; x(0) = 3, x'(0) -1

A: Given that d2xdt2+xe0.01x=0, x0=1,x'0=1; x0=3,x'(0)=-1. (i) So, the equation can be written as,…

Q: 1 | t(t + 3) dt -1

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Q: xy3dx+(y+1)e-xdy=0

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Q: Integrate (x^2)*(e^(2x))

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Q: Find d2z/dxdy of z=ln(x2-y)

A: Partial differentiation with respect to a variable of an expression is carried out by…

Q: (26ー1) 不t8

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Q: t - 1 (a) f(t) = 1 + logs %3D V8 /8-t

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Q: 10. (x2+y)+(x+ey)dydx=0

A: We have given the equation;

Q: 1- yln ydx + (1+ x² )dy = 0

A: ** As per our guidelines we are allowed to answer only one question a time. Kindly please re-post…

Q: XA - ХА + yl th

A:

Q: 9. (yexy - 2y³)dx + (xexy - 6xy2 - 2y)dy = 0

A: The given differential equation is exact, so solve this by the procedure of exact differential…

Q: 1. Evalute +oo dx. /x² + 2 -00

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Q: -5x Integrate x² e

A: We have to find

Q: 5Tanx+13=2ZTanx Lineer (23inx+13)-(2605x)=0 CSCX-(secx-2)=0 Fackr 20033X +C05X-1=0 uva Quie…

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Q: Зу" — бу' + 6у %3 еt sec x -

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Q: iii) ä(t) – 9x(t) = 0, x(0) = 1, ±(0) = 0 -

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Q: 1x x2 SI x +1)dzdydx 00-y2

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Q: 1. Iflx + 1| 1 e -3 2

A: We can solve the inequality in order to get the solution of given problem.

Q: 8y dy e2y

A: topic - definite integral

Q: ) dt 5e + 1+ t2

A: Take the help from standard form of integration and simplify.

Q: 1. x²yy' = ey =

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Q: dy √e²y-1 S

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Q: a) esin 7z dx 2e-2 b) lim 5x 2e-2 c) Sx+5 I-0 5x+5

A: Since you have asked multiple sub parts, according to our company guidelines we are supposed to…

Q: 3x+ y = 3 12. priiqe X- 2y = 8 | madeve

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Q: integrate x^(2)  * e^(3x)

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Q: 'a-x - dx atx valuate

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Q: 3(1 + P) = 2ty(y³ – 1) dt %3D

A: Let us consider the differential equation dydt+P(x)y=Q(x)yn It is known as Bernoulli's equation…

Q: Salve 6y"o)-5y'Lx)+Yx)= esinx+ cos2X with

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Q: Eveluet I= dx dy I+x'ダノ Cali calia い

A: The given integral is: I=∫02∫y4-y2 11+x2+y2 dx dy

Q: 7x Y3D3-5x +9e* dx

A: See the details solution in below

Q: elser (i) E[X] (ii) E [(X – 1)21 (iii) E [3X – 1]

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Q: efined by. Hn(X) +h. iu

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Q: 1+ 2x dx. Compute x2

A: Now we have to compute   =∫1+2xx2dx=∫1x2+2xx2dx=∫1x2dx + ∫2xdx=∫x-2dx + 2∫1xdx                ......…

Q: 2 x²e¬2® dx. Compute

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Q: ~10 xe Ax) = Sg" -dx (x + 2)(x+3)(,² – 1)

A: The given problem is evaluate the given definite integral using Simpsons 3/8 rule.

Q: [eln(==+*) + (t + 3)²]dt

A: ∫elnt3+t4+t+32 dt

Q: (y/x+6x)+(ln x−2)y′=0,x>0

A: Consider the given differential equation.

Q: -1 2 and y = 1 3 -y 6. x = -3. Compute (E) y. (-1)

A: To find ((x.y) /||y||^2) y For the given vectors.

Q: X+x- L-X+, dt 2 x²-1

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Q: Integral 1. xp x²(x - 1)

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Q: 11) y"-y=- %3D (1+e ")

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Q: 1 Jx(х + 4)+

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Q: Find an antiderivative. x² + 1 x2 - 5x - 6 |

A: Antiderivative means integration. Here, the method of partial fraction is used for integration.

Q: ∫ 3e^(5t) dt

A: The given integral is ∫3e5tdt

Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.