The functions y1(t) =t² and y2(t)= t° are solutions of the homogeneous differential equation t?y" – 4ty' + 6y = 0 on (0, 00). When using variation of parameters with y = u1(t)t² +u2(t)t³ to find a solution of the nonhomogeneous lifferential equation t'y" – 4ty' + 6y = 4t³, | vhat is the function u, (t) ? (1) 4 (2) –4 4 (3) (4) t2 (5) –4t (6) –4t?

Q: State the order of the given ordinary differential equation. cosh(4/y) - 5ln(18y)y" = 2cos(5yx) -…

A: Given: cosh(4/y)-5ln(18y)y''=2cos(5yx)-y12y'+4x To find: Order of the given ordinary differential…

Q: The function y = t² is the solution to the differential equation t²y" — t(t+4)y' + 2(t+3)y = 0. - 19…

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Q: (c) and Y2(t) 7. The functions Y₁(t) = t and Y₂(t) = tet form a fundamental pair of solutions to the…

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Q: 3. Given that y₁ = t−¹ is a solution of 2t²y" + 3ty' — y=0, t>0, a) Substitute y = v(t)y₁(t) into…

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Q: 3. Solve the differential equation subject to the given conditions. d² y dx² a) b) d² y dx² +36y= 0,…

A: As you didn't mention the question number to be solved so I solved two questions. For remaining…

Q: y" + 16y = sec(4x). a. Find the most general solution to the associated homogeneous differential…

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Q: show, by direct substitution, that the given functions y1(t) and y2(t) are solutions of the given…

A: Given differential equation y''+4y=0  y1(t)=cos(2t)     , y2(t)=sin(2t)

Q: Find the function y = f(t) passing through the point (0, 10) with the given differential equation.…

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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.