dy りー! り(-)ニ。 x+3 2, xy' =1+X ら(4)=0

Q: 9. Solve d²x dt² + 4x + 5y = 1²; d²y dt² + 5x + 4y = t +1.

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Q: Find the general solution valid near x=0 (x2 + 4) y" + 2xy' -12y = 0

A: We have to solve given problem:

Q: 8x²y" + 10xy' – (1+ x)y = 0

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Q: Solve: dy 6- y") +. onn 13-1 Ordineiy Dibgerential equation

A: The solution of the differential equation can be found with the help of the separation of the…

Q: y" - 6y' + qy 2,

A:

Q: Use variation of parameters to find a general solution: y(3) – 4y = et.

A: Given differential equation: y3-4y'=et         ...(1)

Q: Obtain the general solution valid near the origin: x(x − 2)y" + 2(x − 1)y' − 2y = 0

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Q: fud General Solution dy-3y=

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Q: 3. Is y(x) = Cisin2x + C2cos2x, where Ci and C2 are arbitrary constants, a solution of y" + 4y = 0?…

A: Given, y''+4y=0 a second order differential equation. To show that y(x) = C1 sin 2x + C2 cos 2x is a…

Q: Solve the initial value prol dy + 8, y(1) = 3 dx y%3D 4 Jx +8x 19 4 Oy=Vx + 8x - 6 Oy=-- - 8x- 6

A: Explanation and solutions is given below....

Q: find general solution. dr/dt= -2tr,         r(0)=ro

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Q: Find a general solution valid near the origin: (x²+4)y" + 2xy' - 12y = 0

A:

Q: What is the solution (ry – r) dr + (x²y + y) dy = 0 when 2 and y = 1

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Q: Verify that ry4 +r - 27 = 0 defines an implicit solution of the DE dy 4ry + 2y* + 3r = 0, dr on the…

A: The function f(x) is a rule that associates or fixes a number to the particular point x. The…

Q: Find the general solution of the DE: dx 6- dt2 + 12- - 8x = 0 %3D - dt3 dt

A: Given ODE is d3xdt3-6d2xdt2+12dxdt-8x=0

Q: Solve (D2 – 2)y =0 O a. y = cqevZx + c2e¬vZx O b.y= "(c,cos/2x+ c,sin/2x) O c.y = cqevZx+czxe¬VZx O…

A: The equation D2-2y=0 represent y''-2y=0 . Consider the solution of the differential equation is in…

Q: What is the general solution of xydx−(x2+3y2)dy=0

A: Topic :- Differential equation

Q: . Find the general solution of (³ + 2y*)y' = 3ya² in implicit form f(x,y) = c. When y(0) = 1, what…

A: We have given differential equation  x3+2y4y'=3yx2…

Q: A Q2 Show that y=x+ is the solution of 3x – x = x+ y. dy dx

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Q: Obtain the general solution valid near the origin: 8x^2y" + 10xy' − (1 + x)y = 0

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Q: (b) If z = 9t²e 4, find dz dt 4

A: NOTE: Refresh your page if you can't see any equations. . take derivative

Q: Find the general solution: dy = tanxtanydx %3D

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Q: 10. y"" + y" = 3 А. 3 В. Зх C. D. 3x?

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Q: Y, = Ax² is particular solution of y' + y" = 1 for A = %3D

A: Here, yp=Ax2yp'=2Axyp''=2Ayp'''=0

Q: 4. Solve the IVP: d?s t3, dt2 A. 20s = t5 + 200t – 100 B. 20s = t5 – 200t + 100 s(0) = 5,s'(0) = 10…

A: Given IVPd2sdt2=t3, s0=5, s'0=10sinced2sdt2=t3on integrating

Q: y" + 4y = 2 sin(6x)+ 6x²e¬3z + 5x,

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Q: Find the general solution of y" – y' – 2y = cosh 2t.

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Q: 2e | 3జy S S dy da = Vsin(zy)

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Q: KIN KIN 0 2 d2 sinr do dr dọ

A: A detailed solution is given below.

Q: Find d²y csinx if dx2 Lm VE2 +5 dt + sinx = y – x secx

A: We can use the fundamental theorem of derivative  In order to solve the given problem.

Q: Solve the IVP y + 2y = 0 if t≥ 1 y(0) 1. Is the solution continuous? = "

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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: 23. (4y + 2t – 5) dt + (6y + 4t – 1) dy = 0, y(-1) = 2

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Q: y" + y = 0, y(0) = 0, y' (5) = 2

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Q: Obtain the general solution valid near the origin: 2y'+9ху'-36у 30

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Q: 2 ydx = 3xdy; when x = -2, y = 1 Ans. y = (x/2)3

A: Given: 2ydx=3xdy ; x=-2, y=1   We know that; ∫1ax+bdx=1alnax+b+C

Q: Suppose ay" + by' + cy = 0 with y(0) = d and y'(0) = k has a general solution y = 4e2 3. What are…

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Q: Obtain the general solution valid near the origin: 2y" + 9ху' — З6у %3D 0

A: Power series solution of the differential equation

Q: (D* – 4D³ +14D² – 20D +9)y = 0 - -

A:

Q: Solve for the general solution xydx - (x² +2y² ) dy = 0 x² = 4y° In(2 ) xy = 4y° In() Option 1…

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Q: The equation X2 - 19Y² = 13 has an integral solution, i.e., there is a pair hat x2 19y2= 13. (proof…

A: We have to solve given problems:

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

A: Double differentiate to prove the given

Q: (D³ + 2D² − 5D − 8)y = 0, when x = 0, y = 0, y' = 0, y = 2 - -

A: Given  (D3+2D2-5D-8)y=0 and when x=0, y=0, y'=0, y''=2. The formula for differentiation is…

Q: What is the particular solution of 2xyy' = 1+y2 , when x =2, y = 3

A: The given differential equation is solved below in detail.

Q: What is the general solution of (D³ + 12D³ + 36D) y = 0 ? Oy = (C1 + C3x) cos 6x + (C2 + C4x) sin 6x…

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Q: general

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Q: 2. u(z) +

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Q: Obtain the general solution valid near the origin: x(х — 2)у" + 2 (х — 1)у' — 2у 3D0

A: The differential equation has singularity at the origin. So we find the solution by Frobienius…

Q: 2ste-tds + (s²e-t – t)dt = 0

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Q: Integrate both sides = S sec²y dy = S dx

A: ∫sec2y dy=∫dx