Solve the initial value problem. x2у" - 4хy' - бу%3D 0, у(1) %3D з, у'(1) %3D 4

Q: 2x" 2x' 4x = 2e

A: Given differential equation 2x''−2x'−4x=2e3t.....1 Divide both sides by 2, we get x''−x'−2x=e3t Now,…

Q: b. S 2*³-4x²-x-3 dx х2-2х-3

A: First we divide the polynomial  using long division

Q: 1. 5х2у" + 23ху' + 16.2у —D 0 2. х?у" + 0.7ху' — 0.1у %3D 0 3. х2у" — 0.7ху — 0.1у %3D0 |

A: Given

Q: у"" - 8y" + 41у'- 234 е 3х, у"(0) %3D 187, у'(0) 3D 29, у(0) 3D 10 3x.

A: Now we solve this below

Q: 3t 2x"-2x'-4x = 2e" 5.

A:

Q: Solve for x: 3x -y = 2 - 3y 2-4y ox = V +2 %3D 2-2y %D 3 - %3D 3. O x = 2 - 2y - 3 3.

A: Let us consider an equation ax+by=c  Then solution for x is given as, x= (c-by)/a

Q: e y" – 2y' + y = 1+ r² 2y' + у 3 + Зе* 1 + r2

A: Given,

Q: 2.) (6x*y+z")² 10

A:

Q: 13x+30= (류,-1) and (-3,) 4. Find the equation that contains 7'3)

A:

Q: 7. (y" + 4y) = 4e3x

A:

Q: y" – 6y' + 9y = 4e* %3D

A: Given, y"-6y'+9y=4ex To solve the above differential equation.

Q: Find real numbers and such that 2.x – 3iy + 4ix – 2 y – 5–10ix = x + y – iy + 2-(3– x)i

A:

Q: 5. y" - 4y = 0 6. y" - 64y = 0

A:

Q: exapy %3D 4-x2

A:

Q: Simplify (5x'yz)

A: Given, (5x3y-2z4)3

Q: y = x2/3 + etanx + 6csc2x

A:

Q: Solve for z. (2-i)z+8z^2=0

A: Given equation is, (2-i)z+8z2=0