The solution of the differential equation using Laplace transform y +16y 0; y (0)=6, y(0)=4. cos(4x)+ sin(4x) 6cos(4x)+4sin(4x) 6sin(4x)+ cos(4x) 6cos(4x)+sin(4x)

Q: cos(x)y' + sin(x)y = 2cos³(x) sin(x) — 1, y(4) = 3√2, 0 < x < 1/17.

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Q: 6 sin(x) + 2 cos(x) = 0

A: We are given trigonometric equation as

Q: Suppose a solution to a differential equation is given by: x(t)=5cos(2t)+12sin(2t) (a) Express the…

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Q: Write the given differential equation in the form L(y) = g(x), where L is a linear differential…

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Q: y" +Zy+3y=sin (3x)

A: Given that,  y''+2y'+3y=sin(3x) The auxiliary equation is m2+2m+3=0m=-2±4-122=-2±2i22=-1±i2…

Q: y′′ + 16y = 32 cos(4x) − 24 sin(4x)

A: The given differential equation is        y'' + 16y = 32cos(4x) − 24sin(4x)…

Q: y' = xy³ (1 + x²)−¹/2, y (0) = 1

A: y'=xy3(1+x2)-12  dydx=xy3(1+x2)-12given  y(0)=1∫xndx=xn+1n+1+c

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.