Find the temperature u ( xjt). in a bar of leng te t which is perfectly insulated everywhere induding the ends x=o and x=T.This leads the Conditions Ux(ost) = Ux (T)t)=0,Further the intial temperature is fo = 3 05X+7 cos 2X.

Q: 54 (b) y =. sin 2x. 4 Find

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Q: Find '(t), given r(t) = (-4e-²t, 4t² + 3, 3 sin(−3t)). r' (t) =

A: Given vector is as follows

Q: slove the DE cos x dx/dy +ysinx =sinx cosx

A: r(x) = y'(cos x)  +y(sinx) =sinx cosx   The complementary equation Put r(x) = 0  is (cos x)y' + (sin…

Q: 2. Find S'and S" for the function: S = + 2t2. Cos(t)

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Q: find the value of so that ky'=3 at y =1- For --=1 x y O 12 3 O o

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Q: X(jw) = 8.8cos (3w) sin(0.5w)

A: Given function is:X(j,w)=8.8cos(3w)sin(0.5w)we have to find the value of X(3,5).value of…

Q: 26) y = tan((T/6)x) Period: TT. -217 -ㅠ TT 21T -2 -1 -1 -2 -ㅠ MCL @01 %24 ElN-

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Q: 1) y : 2x0

A: Since you have asked multiple questions in a single request so we will be answering only first…

Q: Find (t), given 7(t) = (– 5t* – 1, 4 sin(2t), 4e*). = (?),

A: Given,

Q: A particle moves on an axis “x" with variable speed v(t) starting from t= 0. Calculate for each…

A: According to question, Particle moves on x-axis direction, We have, Variable speed, v t = 10 + 4…

Q: Find a particular solution of the equation y4 -y3 - y" - y' - 2y = 8x^5:

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Q: 2TT TT 2 5 cos o j ê sin@dr ded@=5TTC

A:

Q: Verify that y = c sec² x is a general solution of y' = 2y tan x, where c is an arbitrary constant…

A: We varify that given solution is solution of given differential equation by differentiating the…

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.