Graph without calculating the solutions/values y" + y' + 4y = &1(t), y(0) = 3, y'(0) = 0.

Q: Calculate y" and y'. y = 0²(20 + 4) y" = y" : II

A: Given function is : y = Ѳ2( 2Ѳ + 4)

Q: 2) Solve the equation y' = Y 4x²y + x

A:

Q: Find y' y = 3x-2 2x+3

A: Given Functiony=(i) (ii) (iii)

Q: Find a particular solution of the equation y4 -y3 - y" - y' - 2y = 8x^5:

A:

Q: Find y'' for y = 4+ or y= (4 + ³) ³. X y"=0 3 5

A:

Q: Solve y" - 2y" - y' + 2y = 0. Include a plot of the solution curves.

A:

Q: Find all solutions to the equation (D^2 − 3D + 2)y(x) = 2e^3x.

A:

Q: Solve :     x²y"-2x(1+x)y'+2(1+x)y = x3

A: Given: The second order differential equation is x2y''-2xx+1y'+2x+1y=0

Q: Determine the solution by the method of variation of parameters. y'''+y''=12e^(2x)

A: y'''+y''=12e2x

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.