D2-4D+4)y = 6e2x / x4 Solve for the general solution of this D.E.

Q: dy Q3. Solve the DE da +y - y? provided that y1 = - is one known solution of the equation.

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Q: Solve (D² – 3D + 2) y = 2e3 +4 sec (e-)

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Q: Solve dy and Evaluate the answer at y=30 and C=-26

A: The exponent rule of integration states that ∫xndx=xn+1n+1+c.

Q: (x+xy²)dxte*, ydy=D0

A: Given: x+xy2dx+ex2ydy=0 ⇒x1+y2dx+ex2ydy=0 ⇒ex2ydy=-x1+y2dx ⇒y1+y2dy=-xex2dx

Q: 28. Solve (D -4D + 4)y = 0 A y= C, + C,e B. y= Ce+ Ce C. y= Cie + Caxe D. y= Ci + Caxe

A: 28.The given differential equation,D2-4D+4y=0

Q: Solve the d.e. using Method of Undetermined Coefficients (MUC) (D² – 3D – 4)y = 30e4x ||

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Q: A. Obtained the general solution. E... 10. (D² – 3D + 2)y = 3x²

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Q: Solve: (4x3y−18x2−y)dx + (x4+3y2−x)dy = 0 a) Check for exactness b) If the equation is exact,…

A: Exact differential equation

Q: Solve the equation by determination method: Inx + ey + tanz = 3 ... (1) 2lnx + 4tanz = 5 + ey (2)…

A: lnx + ey + tanz = 3                              ...(1) 2lnx - ey + 4tanz = 5…

Q: Solve this DE (D2+2D+2)y = e-xcscx

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Q: 1. Give the general solution of (D5 + 2D4 + 7D3 – 4D² – 26D + 20)y = 0

A: First I have find the roots of the auxiliary equation and then according to the roots find the…

Q: Solve (D5 – 2D4 + 4D³ – 8D²) y = 48e-2 16 sin (2x) - = A- B I = E E E P & O

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Q: (3e3ty− 2t)dt + 33tdy = 0

A: The differential equation is given as (3e3ty-2t)dt+e3tdy = 0 Compare it with Mdt+Ndy = 0 then M =…

Q: Solve the following by Substitution Method. (Complete solution) b. dy/dx = (-5x + y)^2 - 4

A: From the given differential equation: dydx=-5x+y2-4...1 Use the substitution method to calculate…

Q: (4D* – 4D³ – 23D² +12D+ 36)y = 0

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Q: Solve sz dz ; c:Iz-1|=1 C

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Q: Q2: solve the equation dx 2x dy y y 3.

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Q: (b) Solve 1 y +-y= 0, t> 0. t

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Q: 2x e dx 4e2a –8e* +5 -

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Q: 3. Solve the DE: Y'=e2x+ 3y.

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Q: 1. Give the general solution of (D5 + 2D4 + 7D3 – 4D2 – 26D+20)y = 0 ="

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Q: Solve the following d'y 8- + 16y = 9e2 dx? d'y dx4 using the method of undetermined coefficients.

A: The solution is given as

Q: Q(4) Find the general solution of dy =(r- y+ 5). dr

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Q: 11. (D- D)y = 0.

A: As per our guidelines only one question can be solved. Please find the solution for Q no 11 below:

Q: nd the general solution to: 2yy -e^ = 0, |

A: The question is taken from the calculus in which we have to find  the general solution of  given…

Q: 2. (D2 + 4D + 5) y = 10e-3x (=D 0, y =4 x= 0, y' =0

A: Explained below

Q: Q-1:B: Solve the initial value problem d?y + 4y = 8x2 ,y(0) = -3,y'(0) = 0 %3D %3D dx2

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Q: Q1: using variation of parameters to solve: * y"' – 2y" – 21y' – 18y = 3 + 4e-t %3D

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Q: 6r+re 5. Solve the equation =m for r. d. %3D

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Q: Q4/ solve the following equations. d²y dy + 81- = 0 dx² dx

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Q: 1. Obtain the general solution unless otherwise instructed · (D5 + Dª – 7D³ – 11D² – 8D – 12)y = 0 -…

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Q: (D² – 3D + 2)y = e2*(1+e2x)

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Q: FIND THE PARTICULAR SOLUTION: SHOW SOLUTION AND PROVE THAT THE EQUATION (y4-2xy)dx+3x2dy=0; when…

A: We have to find the solution

Q: 28 Solve the equation : + 12y + Jy? + 12x = 33, x + y = 23.

A: Introduction :

Q: dy (t2 – 26t + 120) = y dt

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Q: A. Solve the following DE by using exact equation method: y = x - y, B. Solve the following equation…

A: Q2. A) Given differential equation is y¯=x-y ⇒dydx=x-y ⇒x-ydx-dy=0

Q: Solve method of undetermined coefficients using (D+AD+8)Y 3X t, z 13e +50X when x-0, y=0, Y=D0 ゾーo

A: Given that, D2+4D+5y=13e3x+50xwhen x=0,y=0,y'=0

Q: dv Solve ax + by + c dx

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Q: Solve the nonhomogeneous equation: (D2-4)y = 2 –8x, when x=0, y=0, y’=5, using undetermined…

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Q: R: Given the IBvp の o<xcL Solve for 4(XE).

A: Using separation of variables and superposition principle

Q: By using method of undetermined coefficient solve (D² – 3D + 2)y = ex + e2x ;D = 4 ? dx

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Q: 1. Solve for y. D B 420 C0y-4 8. Find MZBCD. 40

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Q: Solve this equation y"+ 2y + 2y = e-t where y(0) = 0 and y'(0) = 0? %3D

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Q: Solve the difference equation A?yn + 3Ayn – 4y, = n² with the initial conditions yo = 0, yn = 2. %3D

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

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Q: (24) Solve : (n²y = 2xy²) dn. - (n²³-3n² y) dy zo

A: Solution

Q: Solve the DE with general solution m''-3m'+2m=0

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

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Q: b) Find the solutions qf th equation 4.1.2 D Ø(D) 1. (D3 – 6D2 + 5D): 2. (4D2 - 3D- 10):

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Q: Q#d4 Solve the D.E. y"+ 25y= lo(cosst-asinst)

A: Given: y''+25y=10cos5t-2sin5t, y(0)=1, y'(0)=2

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.