Find the L(e"(1+ t)²). ,2t (s-2)3 (s-2)2 3 2 b) 8-2 (s–2)³ 2 3 (s-2)2 2 (s+2)³ 2 (s–2)² d) 2 + 3 (8–2)³ +.

Q: D2 – 5D +6)y=3xex+2x2 , y(0)=0,y,(0)=1

A: Given differential equation is homogeneous ordinary differential equation. To solve this equation…

Q: (d + g) Q² + (e + s) PQ = a (d + g) PQ+a(e+s) P² + (b+ f) Q+(c+ r) P. (15) By subtracting (14) from…

A:

Q: Find A. C. d³y dx³ given y = 48(x²-3) (x² + 3)4 24x(x²-3) (x² + 3)4 2 x²-3 B. D. -48x(x²+3) (x²-3)4…

A:

Q: 7(t-3)=6t+21

A:

Q: Sx(x-2)/xr³ – 3x² + 5dx

A: By using substitution, we calculate the given integral.

Q: 5. Find mZHGI. F G (7x - 1) (4r + 3)"-

A:

Q: 16. When (2x- 3)' is subtracted from 5x, the result is x²-12x-9 2x - 12x + 9 3x + 12x-9 4) x + 12x +…

A: Given:         2x-32 is subtracted from 5x2 is    here 2x-32 is in the form of a-b2=a2+b2-2ab

Q: 6. Simplify. a) (2x - 3x2- 6) + (6x – x³ + 4x² + 5) b) (x² – 4)(2x² + 5x - 2) c) -7x(x² + x - 1) –…

A: Given that -

Q: 2 d) ²₂t(t4 +3t)dt -2

A: We need to solve ∫-22t(t4+3t)dt

Q: 4. What is the constant value (the term without a variable) of the product (3x - 1)(2a² – 6æ – 9)?

A:

Q: (3) J -x² + 4x 2 x³ + 4x² + 4x + 3 dx

A:

Q: 2 =[41] −1 4 If A = find (AT)-¹.

A:

Q: 3(z+5)=12

A:

Q: The parametric equations x=t+2 and y=+²+ 3t represent a plane curve. Which of the following…

A:

Q: (c) 0$ y = cos (√√x² +1) (d) y 2x 2x +1

A: Given that: (b) y=exx2(c) y=cosx2+1(d) y=2x2x+1 The quotient rule of derivative is…

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.