When do the following integral equations have solutions? 3. u(z) = f(x) + A S u(t)dt.

Q: Find the solution. dy x2-y?=2xy dx -2 A -1 B y = C y = 2.

A: Given Differential equation is x2dydx - y2 = 2xy

Q: 9. Find the general solution of the system of differential equations 2 2 1 2 5 2 1 2 2 d X%3= dt 2 1…

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Q: Check the DE if it is exact or not. Solve it (if it is not exact use the method by using the…

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Q: (n) If g(x) = o f(t) dt, then g(2)

A: We plug x=2 in the given function

Q: Ydx - xdy + x(2 - y)dy = y? ey dy %3D

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Q: 7. Let D = acting on infinitely differentiable functions, i.e., for a function f(x) * be the…

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Q: - particle's position for t > 0 is given by s (t) = 2t³ + 2t² – 5t +2. What s the acceleration at t…

A: Given query is to find the acceleration ate t= 1.

Q: (t² + 2t) dx = 2x + 8, x(1) = 1 dt

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Q: Linear First-Order D.E. | 6. Solve the equation: t2 dx – (tª In t + 1 - 3tx) dt = 0, x(1) = 0. %3D

A: The given differential equation is: t2 dx-t4 ln t+1-3tx dt=0 ;       x(1)=0

Q: the general solution of the differential equation Find (D2-6D+8)f=e :e-2x +sinsメ

A: Given differential equation is D2-6D+8y=e-2x+sin5x fD=D2-6D+8, Qx=e-2x+sin5x

Q: solle не ۱/۱ 2 z² + 1 ²+1 dz 3 3 cus x sin³ x dx で T=T [く] M

A: We have two integrals to solve:∫ (1/2) z² + 1 dz∫ sin³ x dx

Q: By using differentials and Linear Approximations: a) Show that the linearization of f(x) = (1 +…

A: Given function f(x)=1+xw+10 we need to show that the linearization of the function at x=0 is…

Q: The order and degree of the differential equation A) 2 and 4 B) 3 and 4 2 and 3 D) 3 and 2 d²y dx2…

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Q: solle не ۱/۱ 2 z² + 1 ²+1 dz 3 3 cus x sin³ x dx で T=T [く] M

A: We have two integrals to solve:∫ (1/2) z² + 1 dz∫ sin³ x dx

Q: dy d²y — 4х — + бу 3D 4х — 3 dx² dx

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Q: dx Use residues to derive the integration of ²1 0

A: 1. Residue at a pole z=a of order 1:limz→a(z-a)f(z)2.Residue Theorem: ∫cf(z)dz=2πi[Sum of Residues…

Q: d²N Solve t di? dN - 2t- dt + 2N = t In t

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Q: d*y d?y 4. dt2 24 dt4

A: Given differential equation can be evaluated as shown below

Q: (2² + a² ) dy |(x2 + a?) + 3y dx; a is constant

A: Given that, There is a non-exact and first order linear DE, (x2 + a2)dy = 2x[(x2 + a2)2 + 3y]dx,…

Q: Classify the following differential equation: e* + 3y = x²y dx a) Separable and homogeneous b)…

A: Solved below

Q: Show that the differential form in the integral is exact. Th (1,2,3) | 2xy dx + (x² -z°) dy -6yz dz…

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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.