dy dt (d) di² + 2- 3— 3t + 2, у(0) — У (0) — 0. dy (е) di? dy + 20y %3D —3 sin 2г, у(0) %3 у' (0) — 0. dt dy (f) + 9y %3D 2 сos 31, у(0) %3D 2, у (0) 3 -9. dr?

Q: 2. Solve the general solution for the First Order Linear DE. удх %3D (еУ + 2ху — 2х)dy

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Q: 1-² dx dy dz se ³ 1 xyz 2-fff(x+y+z)dy dx dz TL 3-fff₂y sinz dx dy dz 6 -2

A: As per Bartleby guidelines for more than one question asked only one is to be answered please upload…

Q: Obtain the particular solution of the DE: 4(3x + y – 2) dx – (3x + y) dy = 0; when x = 1, y = 0…

A: Gg

Q: If f(x, y) = 2x² – 8y², then the total differential of f at x = 1 and y = -2 is : - O df = 32 dx + 4…

A: In total differential take the derivative of each terms, put the given values and simplify.

Q: The solution of (1+y²) + (t- elan-ly Y =0 is: -1n dy %3D dt Select one: a. 1 t 3D elan-ly e2tan-ly O…

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Q: Solve 3rd order ODE with forward and backward eulers method. from t = 0 to 0.1, h = 0.1, y0) = y(0)…

A: The third order equation is d3ydt3-2y=0. Consider dydt=p, d2ydt2=q⇒p'=q, q'=2y By Forward Euler…

Q: What is the differential equation of the orthogonal trajectories of the family of curves x2 - 3xy-…

A: Given family of Curve is x2-3xy-2y2=C

Q: dx 2х — dt dy – y = 6e3t, dt. dx 2 dt dy 3x + dt - 3y = 6e3t; %3D x(0) = 3, У (0) — 0. %3D

A: As per our guidelines, we are supposed to solve only first question. Kindly repost other question as…

Q: What is the differential equation of the orthogonal trajectories of х3 — Зху — у3 — с? (1) (x +…

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Q: dx dy (a) dt di -y = 6e3t, 2 dt -3x +-3y = 6e3t; dt x(0) = 3, y(0) = 0.

A: As per our guidelines, we are supposed to solve only first question. Kindly repost other question as…

Q: 4.Solve the pair of simultaneous equations dx =xy-t, x(0)=1 dt dy = x+t, y(0) = 0 dt From t=0 to…

A: You don't mention any method by which we can solve, so i use simple Iteration method Euler's Method

Q: 30 -20 -10 Compare dy with (r-y} dydx 10 20 30

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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: The order of the differential equat 2x2 - 3+y = 0 dy + y = 0 dx2 dx O not defined O 2

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Q: Find the differential dy: y = In(sec² ( 3"-2*+5)). Find the differential dy: y = In(sec? ( 3-2x+5…

A: We have to differentiate given function

Q: 36. Using the approximation dy dy h dr * Yn+1- y. and that dr 1, y = 2 when r 0. Then, y A h- 2 h+ 2…

A: Please see the answer below.

Q: Find the solution of dy dy +2 - 3y = 2e2", y (0) = 0, y' (0) = 0 dt2 dt

A: Since you have asked multiple questions, we will solve the first question for you. If you want any…

Q: 1. y" - 2y' - 3y = 5e¹, y(0) = 1, y'(0) = 0 2. y" + 2y + 5y = 3 sin(2x) 3. y" - 4y + 4y = -7x+4x²,…

A: Since you have posted multiple questions. As per guidelines we"ll solve only  first question. If you…

Q: d² y dt² + 3 dy dt +2y(t) = 2e²¹ ; y(0)=0_

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Q: d'y dt2 dy + 4 + 3y = 20 sin(t) where y(0): -2, (0): - 4. Find the solution to the IVP %3D

A: firstly we find out CF and then PI and  general solution is  y(t)=CF+PI

Q: Find the general solution of dy 3 -my – ny | dt

A: We need to find the general solution of the differential equation dydt=-my-ny3. The solution is…

Q: (y')² – 3yy' + xy = 0 12 +y = x \dx², S + (S + = 0 dt² dt² dy x*y" + xy" = ex ds t2 \dt², () - t=1 –…

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Q: The homogeneous equation with constant coefficients of least order that has y = 2e3t + 3 sin(3t) +…

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Q: - d² y dt² y (0) = 10 dy 4 - 5y = e-3t sin(4t); y (0) = 3, dt

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Q: d*y 4)5t - dt4 +3r²( - (sin t)y = 0 -)³ – (sin t)y = 0 dt 5)(sin x)y² + 2 y = 3x' – 5 6) ху ? + 3 ху…

A: The order of the differential equation is the equal to the highest order derivative available in the…

Q: sin(2t + ) dt e21-3 4 7 4 4 64e 7

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Q: 5. Solve dy+dy =5 with y"(0) = 0, y'(0) = 2, dt dt У (0) %3D0

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Q: e. dt2 d²y dy + 4y = 8t – 10, y(0) = 1, y'(0) = 7 dt f. 3- dy 3– 2 - y = 2y – 1, y(0) = 7,y'(0) = 2…

A: Since you have posted multiple question and according to guidelines we will solve only one question.…

Q: dy - 4 - 5y = dy -3t sin(4t) ; y (0) = 3, y (0) = 10 dt2

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Q: dy + 2 dy + y = sinh 3t – 5 cosh 3t ; y (0) = -2, y (0) = 5 II %3D |3D | dt? dt

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Q: d?y 4- dt2 dy dy (-2) 9. + 28 + 49y = 0; ; y(-2) = 2 ; = dt dt 2 d?t dt + 9 dx dt (0) t(0) = 3; dx…

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Q: 3. Integrate! 12e dt a) ] 5e041 -0.21 b) c) f- dx 6r dr 3r? .$1+ In 3x² d) [Vcot*0 •csc² 0 do 2+…

A: Using Methods Of Integration

Q: (1 + cos 2y) dr - 2r dy = 0, y(1) = i %3D Oy = Arctan 2 O y = Arctan O y = Arctan ( 1) D y = Arctan…

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Q: 7. Obtain the particular Solution by satisfying the conditions indicated. 3x dy; when x = 2, y = -1.

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Q: 21. xy' = 3y +x* cos x, y(27) = 0 22. y' = 2xy + 3x² exp(x²), y(0) = 5 = 4x* %3D %3D %3D %3D 23. xy'…

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Q: (ye*y)dx + (xe*y + sin(y))dy = 0, y(0) = t exy + cosy – 1 = 0 ЗехУ — сosy — 2 %3D 0 Option 1 Option…

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Q: cos v f(x, у, 2) 3D xz2 af af 2 cos y Cosv siny df = - = - = - dx x2z2' dy dz xz3 XZ af cos v %3D af…

A: Topic:- partial derivatives

Q: 2. y' = y sec x ; 3. у(3x3 — х + у)dx + x?(1 — х?)dy %3D 0 4. у(2х — у + 1)dx + x(3x — 4у + 3)dy — 0…

A: 2) y'=y secx this can be written as dydx=y secx⇒dyy=secx dx integrate the function ∫dyy=∫secx dx…

Q: 5.Express this model of an electric circuit d²y dt² dt As a pair of first order equation +6+5y=sin…

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Q: d's 元 =-4 sin 2t-- 2 s'(0) = 100,s(0) = 0 %3D dt?

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Q: •ý -2ý +y= ě sinx %3D Ans: y=ě +2xě - ě sinx • ý -uý ruy = 12 /* %3D e 2X 2 ZX .2 +C2 X e + 20

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Q: me general solution of (D²-2D+1)y=2sin > A y=c1eX +C,xe* + sinx+cos x y=C1eX +C,Xe* + sinx ©…

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Q: 5.Express this model of an electric circuit d²y dy +6 +5y = sin10t, y(0)=0, y'(0)=1 dt² dt As a pair…

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Q: 4. (4y+ 21 - 5)dt +(6y+41 –1)dy = 0, y(-1)= 2 cs

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Q: 7.Obtain the particular solution of (1 – xy)-2dx + [y? + x²(1 – xy)-²]dy = 0 when x = 2, y = 1

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Q: 6. Find S(3y – y³) (1– y?)dy sin ycos y 7. Integrate: J sin² y dy 8. Find 3 S(5 - 3y-5)²dy

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Q: By (d) dy 2- = 3t + 2, y(0) = y'(0) = 0. dt By +4 dy + 20y = -3 sin 2t, y(0) = y'(0) = 0. (e) dr² dt…

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Q: d²x + 16x = 1 + 2 sin 4t dt2 dx (0) = 0 x(0) = 0, %3D dt

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Q: 5.Express this model of an electric circuit d² y dy +6¹ +5y=sin10t, y(0)= 0, y'(0) = 1 dt² dt As a…

A: First I have introduced two functions and then find pair of first order differential to the given…

Q: d²x + cos(t)- dx sin(t)- + sin(t)x = tan(t) dt dt2 x(1.25) = 6 dx = 5 dt 1.25 has a unique solution…

A: The differential equation  d2ydt2+ptdydt+qty =rt                    .......1 with conditions yt0=y0,…

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.