O O O O O O Consider the equation y" – y' - 2y = 8t2. which O In order to find the general solution, we need to 2t t2 is a solution to the equation. -4t? + 4t - 6 is a particular solution. 2020et + 2021e2t - 4t2 +4t - 6 is a solu If Y1, Y2 are two solutions to the equation, ther O 4e2t – 4ť² + 4t – 6 is a solution. O y" – y' – 2y = 0 is called the associated hom %3D

Q: (4ху? — 1)x2 + у(2x4 + у)у' %3D5; у(1) — 1

A:

Q: Solve y" - 2y + 17y=0

A: If the roots of the characteristics equation are complex numbers a±bi, then the general solution of…

Q: Solve the equation by using a u-substitution: x 5 + x5-2=0

A: The given equation is: x25+x15-2=0⇒x152+x15-2=0

Q: Jenny solved the equation 1 - (2x + 4) = -4x + 5. Her work is shown. %3D

A: Given 1-(2 x+4)=-4 x+5

Q: (4n8x3)-3 =         How do I solve?

A: For the negative exponent, we can make the reciprocal of the expression.

Q: Solve for X in the equation, where -4 -3 A = and B = 5 3 -3 -2 -5 ABHTOMA RD 2X + ЗА 3 В

A: The given matrix,A=-4-3203-3 and B=0250-2-5

Q: Solve the Equation: x²-12x+39=0 1. (-5, 4) ○ 2. (-7,8} O 3. (8,-4) ○ 4. (6, -5}

A:

Q: 13) Choose the correct answer. You are working with your friend who finds the solution of –# + 2y =…

A:

Q: -1 0] -2 6 Use A = 10 and B = to solve the equation 3A – 2X = B. -4 13

A:

Q: VZ A2 + B2 =0 A2 + VZB2 + C2=0 B2 + VZ Cz = 0

A: We have to solve the given system of equation.

Q: Solve y -x + 2y z = ++ W W 2z+ -Z + W 3z + 5w W 1242 2 4 = 2

A: To solve the equation.

Q: Solve each equation

A: To solve the given equations.

Q: If v = 2i - 3j+ k and w = 3i - 2j - k, find ● VXW K j 2-3 1 3-2-1 3 11 2 + 2 3 - 3 2 = (3 + + 2); -…

A:

Q: ーy=5 5x-y=3 than one sol al solution, u

A:

Q: (15x - 8) 226

A: Given,

Q: 9. Solve using u-substitution: 2x-2 + 5x-1– 12 = 0

A: Given 2x-2+5x-1-12=0 Solve using u- substitution

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.