Let y1, Y2 be two independent solutions of (t – 1)y" – ty' + y = 0. If W (y1, Y2)(2) = e² , then W(Yı, Y2)(3) = (A) 2e² (B) 3e (C) e? (D) 2e³ (E) None

Q: are both solutions for the homogeneous DE: The functions y1 =e" and y2 =e y" - 16y = 0. Then, the…

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Q: Exercise : 4 3 a) Evaluate , S /1-х2 |1-x²-y² .-3(x²+y²+z²)² dz dydx

A: Triple integral is used to find the volume bounded by a region. There are many methods that are used…

Q: 6. Find the general solution of X Ury -Y Uyy = Uy %3D by using the change of variables: v = x, w =…

A: Given: The partial differential equation, xuxy-yuyy=uy   To find: The general solution of the given…

Q: 2. Find general solution of the DE y" + 3y" + 3/ + y = 0

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Q: ) Obtain the general solution of y" + 2y + y = e² In r

A: In this question, the concept of the differential equation is applied. Differential Equation A…

Q: 3. Obtain two linearly independent solutions valid near the origin: 3xy" +(2-x)y' - 2y = 0

A: As per the question we are given the following second order ODE : 3xy’’ + (2-x)y’ - 2y = 0 And we…

Q: d²z 2+ 3-2z = te-2t ; z(0) = 0 z'(0) = -2 dt2

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Q: ) y, = x2 IS ODE X²y"+2y-6y=0 SOLUTION OF THE USE THE REDUCTION OF ORDER FOAMULA TO FIND A SCCOND…

A: We have to use reduction formula:

Q: Find the general solution of 2x°eWx + x³y²_ y x*y x + y Сх— х In(x?), a) Oy= In x + y Сх- х In(x?),…

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Q: Find two linearly independent solutions of y" + 5zy = 0 of the form y1 = 1+ azr + açz® + ... y2 = x…

A: Consider the differential equation          y''+5xy=0 Find two linearly independent solutions of the…

Q: Find the wrong Kian W(y1,y2)(t) of y1 and y2  Where y1=t and y2= e^t are solutions of…

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Q: 3. Use your solution from Part 2 to give solutions to the IVPS i. y" + 2y' + 16y = cos 3t, y(0) =…

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Q: Let y(x) be the solution of y' = y − 6x such that y(2) = 2. Using a step size of 0.5, set y0 =…

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Q: Find a particular solution to y" + 5y' + 6y = lte".

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Q: x²y" +xy' – y = T

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Q: EXERCISE 1. dy ry+y Find the general solution of dr

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Q: Obtain 2 linearly independent solutions valid near the origin for x>0 2хy" + 5(1 — 2х)у' — 5у %3D 0.…

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Q: 7. Show that y(t) = c,e¬# +czte¬2# is a solution to y" +4y/ +4y = 0. Determine the constants c and…

A: The given equation is y"+4y'+4y=0. A second order linear, homogeneous ordinary differntial…

Q: Suppose we are given y₁) and y2(x) (with y₁ ‡ y2), which are two different solutions of a…

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Q: Verify that u = 3x² +3r – 12t – 8 is a solution of heat equation: u, + 2u, = 0.

A: A solution to an equation is the value that satisfy the equation. Suppose that y1 is a solution to a…

Q: y" - 5y' = x - 2, when x = 0, y = 0, y' = 2

A: We have to solve the given differential equation.

Q: 14.Show that any separable equation M(x)+N(y)y′=0 is also exact.

A: Given: Mx+Nyy'=0

Q: - y" - 4y - 12y = e

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Q: Solve. a) y - e" cosy b) +2y= + 2y 6e **-+(Let u - )

A: Since you have asked multiple subparts of this question, we will solve the first three subparts…

Q: x°y" – 3x'y"+ 6xy'– 6y = 0 -

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Q: 2. Obtain the general solution of the following equations: (i) x²uxx + 2xyuxy + y²uyy + xyux + y² uy…

A: If you want I solved other option please post it again

Q: Q1 : Find the solution of x, y, z by using Gramer's Rule. 3x + 2y – z = 1 x - y + 5z = -2 2x + y = 3

A: As per our guidelines we need to solve only one question. Please repost the remaining questions as…

Q: 22 To solve y =cy - by' change to u= 1/y?. Substitute for y in um - 2yly³ to find a linear equation…

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Q: Find the solution of z'y" + bay + (4 + 4r)y - 0, z > 0 of the form where co 1 Enter n1,2,3,...

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Q: Find two linearly independent solutions of y" + 3ry = 0 of the form Y1 = 1+ a3x³ + a6x® + · .. Y2 =…

A: We find two linearly independent solutions of the given differential equation  y"+3xy=0.......(1)

Q: dr = -4rt whent=0, r=r, dt Obtain the particular solution of - %3D

A: we have to use separation of variable

Q: Test 1. y" - y - 2y = e by D- operator method 2. y" - 3y' +2y = ex + 6x3 - 2+ 3sin(4x)

A: 1. Now we will solve the differential equation. The genaral solution: =…

Q: 1- , L, v² e*dydx 2- S S マーーー ydxdzdy a>0

A: Explanation of the solution is given below...

Q: Show that y = In (x) is a solution of xy" + y² = 0.

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Q: (T^2-x)dt-tdx =0 when t=1 x=5 Ans,: x=1/3t^2 + 14/3t please show solution

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Q: 2. Use substitution to solve the second order y(0)=1 and linear IVP y"-y=0 with y'(0)=0. Hint: Let…

A: Given that, Second order differential equation is, y'' - y = 0…

Q: Verify that u(z, t) = f(e'r) solves the initial value problem (a,u + z8,u = 0, u(x,0) = f(x).

A: Take the partial derivatives of u(x,t).

Q: Verify that y = 1/(x+ C) is a solution to y'= -y², where C is some constant. Find the particular…

A: Given that: y=1(x+C)

Q: 2 Verify that for r > 0, y = r is a solution to yy = x. V3

A: Double differentiate to prove the given

Q: This is the solution of y" + 4y' + 3y = 8 (t – 2) , y (0) = 0, y' (0) = 0 O y = [e-t-2) –e-8(t-2)] U…

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Q: az (b) Solve and ди by applying chain rule if z = In(x² – 2y), and x = u + v, y = e". dv

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Q: 9. Ify,(x)= sin 2r and y, (x) = cos 2x are two solutions of y"+ 4y 0, show that y, (x) and y, r) are…

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Q: yp=u1x+u2x^-2 is the particular solution proposed for the nonhomogeneous Cauchy-Euler equation…

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Q: Compute the general solution valid near the origin ((+4x² )y" - By = O 'y= s{1 - 4x°) + a»\x=…

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Q: 3. Find the general solutions of, dy_x+y dx х-у, а.

A: given differential equation is  dydx=x+yx-y

Q: Determine a general solution to the Cauchy-Euler equation z'y"(x) – 2y(z) = 3z² – 1, z>0.

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Q: Find general Solution of y + +y+ 4y = Ct1)e Using method of vanafion.

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Q: Find the general solution to (D5-2D3-2D²-3D-2)y=0 O y= e-X(Cı + Czx) + C3e2X + C4COSx+ Cssinx…

A: Sol:- This can be written as :- D5-2D3-2D2-3D-2=0D+12D-2D2+1=0D+1=0  or   D-2=0  or   D2+1=0The…

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.