For the ODE ty" – (1+ t)y' + y = t°c", t>0 verify that y = 1+t and y2 = e' are solutions of the homogeneous equation, then find the general solution by using variation of parameters.

Q: Differentiate 2 Y = t² + 5÷t² - 4t² + 3 Y' = ?

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Q: Find all solutions of the DE y"– 12 y '+36 y=16 te°* (where t is a real constant)

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Q: Determine exact solutions for the equation 2sin'x – 3sinx +1 = 0 in the interval xI [a, 3n].

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Q: xy2 y' = ey + sin y dy = dx x+y y' = x2

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Q: Solve y" – 4y' + 8y = e2" + sin 2x 3.

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Q: ng the method of undetermined coefficients, find the particular solution y, for the NHLDE Y'"-…

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Q: Without solving, classify the following equations as to: separable, homogeneous (the gree), exact,…

A: Note: Since you have posted a question with multiple sub-parts, we will solve the first three…

Q: homogeneous equation

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Q: Find a general solution of the equation: 3x?y" + 2xy' – 2y = 0

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Q: Solve for y: y'=7y²², y = 3 when x = 1

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Q: Verify that y = Ce^−3x is a solution to the ODE dy/dx + 3y = 0, where C is an arbitrary constant.

A: Step 1:The provided ODE is:dxdy​+3y=0   .........(1)It is needed to verify that y=Ce−3x is the…

Q: Find general solution. y" + 4y = 5 sec ² (2+)

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Q: Consider the Riccatti equation  v'= v^2-7v/x +8/x^2 a) Use the substitution  v= y'/y  obtain the…

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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.