y" + y = >(-1)"5(t – 2rn), y(0) = y/(0) = 0 n=1

Q: (12) If y = a X"-b X*+1+5 is a polynomial and a » bER , then may by represent dX" by one of the…

A: n order derivative

Q: 3. Find syz for ys = In(x + yz) – xcoth-1 log ().

A: Given : Let us consider the given value as,  ys=ln(x+yz)-xcoth-1logzy

Q: on y=1-x+y=xy given that y(0) = -3

A: Given differential equation 12y' = 1 - x + y - xy Given that y( 0 ) = -3

Q: √√3+ rdr then 0 (2)=√√3+230 I X

A:

Q: Find the GS for x³y"" + 6x²y" + 4xy' — 4y = 1 − x − 2x² -

A: Solution:-

Q: If ƒ(x) then f"(x) = · = 0 X (t³ + 5t² + 1) dt -

A:

Q: -3/2 -¹² (2²³ + 2x) da with y(0) = 0, y(3/2) = 1. (c) J[y] = =

A:

Q: Let Y(t) = be the solution of , 6 1 Y, 5 4 -2 - Y' Y(0) 8 Write x(TT/10), round your answer to two…

A: To solve this problem first we write the system as a system of linear homogeneous differential…

Q: Solve y" + y = 8(t – 7) – 8(t – 27), y(0) = 0, y' (0) = 1.

A:

Q: dy 5. x- 3y = x². dx

A: (5)We need to find the solution of given differential equations

Q: x²yy' = (y² - 1)3/2

A: Given that, x2yy'=y2-132 We can solve this by using variable separable method. ∫xn dx=xn+!n+1+C

Q: (x"^y2/5)20 1/4 2/5 (x' (2) 2

A: since you have asked multiple questions in single request so we will be answering only first…

Q: y′=(3t2+4t+2)/2(y−1),y(0)=0

A:

Q: y" – 2y' + y = -3 –x+x, y(0) = -2, y(0) = 1.

A:

Q: (e) y(ª) – 4y "= 5x² -e2* (g) y(“) +8y '= 4

A: The given differential equation is y(4)-4y''=5x2-e2x

Q: If f(x) = =√(t³3 + 3t² + 6) dt then f"(x) =

A:

Q: (a) Solve y" + xy + (2r – 1)y = 0, %3D near z = -1, if y(-1) = 2; y'(-1) = -2.

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Q: (2 11) dx (x+2)* (x-1) *

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Q: y(4) - 4y" + 6y" - 4y+y=0; y(0) = 0, y'(0) = 1, y'(0) = 0, y" (0) = 1

A: The Laplace transform is used to find the solution of the linear ordinary differential equation with…

Q: If r(y) = e³y² +3 find r'(y) =

A:

Q: 1. y = 4* y = 1. • 3* %3D 3. f(x) = 3*+ 1

A:

Q: (3) y "'- 2y "– 4y '+8y = 6xe²* %3D

A: Note: " As per our guidelines we will solve only first question . If you want any specific question…

Q: '5 '5 '5 If f(x) dx = 33 and g(x) dx = 14, find [2f(x) + 3g(x)] dx. %3D

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Q: 7. If y = e*², then d²y dx2 boins9 (A) (2x)(x² – 1)e*²-2 stod beniu (B) ex2 (C) 2xe*2 (D) (2 +…

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Q: By= In(Cx-2)

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Q: e + xy + 4x = 1 ise y"(0) =?

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Q: For the difference equation given by y(k + 1) + y(k) = 3 (1/2)* with y(0) = 1 Find the expression of…

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Q: (11) 10y" - 3y' – y = 0

A: Explanation and solutions is given below....

Q: If g(t) = -3t 5t² - 6 find g(0) = g' (0) = g" (0) = -

A: Since you have asked multiple part question, we will solve the first 3 part of the question for you…

Q: d (1+t³) 5. dt {262+ 1)A}

A:

Q: If f(4) = 3 and f'(x) 2 3 for 4 s xs 9, how small can f(9) possibly be? (9) 2

A:

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.