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

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

A:

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: '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 +…

A:

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.