3. Solve the initial value problem: y" + 5y' + 4y = 0, y(0) = 0, y'(0) = 1

Q: B. Solve x' = 01 1 54 x + 12e4t 18e4t

A:

Q: 5) Find the general solution of the following equation y" +8 y"-9 y=0

A:

Q: 1. Solve Cauchy-Euler equation. r²y" – ry' + y = 2x

A:

Q: Find the general solution to y''-1=0

A: y''-1 =0y'' = 1y' = ∫1 dxy' = x + By =∫(x + B) dxy = x22 + Bx + A

Q: (2xy² + 2y) + (2x²y + 2x)y' = 0

A:

Q: Solve y" + 2y' + 4y = 0.

A: According to the given information, it is required to solve the given differential equation.

Q: Solve the initial value problem: 9y" + 6y + 8y = 0, y(T/2) = –2, У(п/2) — —1. Give your answer as y…

A: The given differential equation is- 9y''+6y'+8y=0

Q: 3. Solve y" – 2y' + 5y = 0, y(0) = 5, y'(0) = –3. %3D

A:

Q: 3. Solve each equation. y(0) = 1, y' (0) = -1 (a) y" + 4y = 0, (b) y" + 5y = 0

A: We have to solve given problem:

Q: + ¹² = 4t, where y'(1) = 1 and y(1)=2. 4) Solve y" +

A:

Q: 2yy" = 1 + (y')² 2

A:

Q: Find the general solution y''-y'-2y=0

A: Given the differential equation y''-y'-2y=0. We need to find the general solution of the above…

Q: Solve y'' − 4y' + 4y = 3e2t

A: Solve y'' − 4y' + 4y = 3e2t

Q: 5. Solve 3y" (x) + 2y'(x) - 8y(x) = 0, y(0) = 6, y'(0) = 18

A: 3y''x+2y'x-8yx=0y0=6y'0=18

Q: Solve y(H) a) Y (6) = y (4) = ? %3D b) y"-y' • 24 ylo)=1;y'(0)=-2 %3D

A: We have to find the solution y(t) from the following  a) y(s)=1s2(s2+1) b) y''-y'=2t, y(0)=1,…

Q: 1. Find a general solution of the first order equation: y'= 3x²y².

A: The given first order differential equation is solved by method of separation of variable.

Q: 5. Solve 2y" - 3y' - 2y = 0; y(0) = 1, y'(0) = -1.

A:

Q: - Sapotri to solve 2x?y" – my + (x + 1)y = 0. n=0 12) Use y =

A: Given: 2x2y''-xy'+x+1y=0. To Do: Solve the given differential equation using y=∑n=0∞anxn+r.

Q: Solve the following IVP. y"'-5y"-22+56=0 y(0)=1 y'(0)=-2 y''(0

A:

Q: 2. Solve y" + 2y' – 3y = 3, y(0) = y'(0) = 1. II %3D %3D

A: given differential equation is linear non homogeneous differential equation with constant…

Q: ii) Solve (x D²– 3xD+4) y = x² given that y(1) =1 and %3D - y'(1)= 0.

A:

Q: Solve (D-2)²(D²+1) y=0,y (0)=1y '(0)=2, y'' (0)=3, y''' (0)=4

A:

Q: 5. Solve the equation y-y'y"=1, given that y=√2 and y'- and y'= when r=0.

A:

Q: Solve  y'' − 2y' + 5y = x2 + 1

A: Solution

Q: 4. Solve (x-2)y" - (4x-7)y' + (4x-6)y= 0, if y₁ = e2x is one known solution? HO The Cystem 2e²t

A:

Q: 8. Solve (a) y' = (3y²)~1 (Hint: Separate.)

A:

Q: What is the general solution to y''+y=0. Show the solution.

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.