find general solutions of the following systems using variation of parameters x' = 3x- y+ sin t y = 4.r y+ cos t

Q: If y satisfies the equation y2+ xy – 1 = 0, then y’ exists everywhere. True or False Justify your…

A: y2+ xy – 1 = 0Differentiate both sides with respect to…

Q: Find the general solution of y"+y = cos(t) (a) Using undetermined coefficients (b) Using variation…

A: Find the general solution of (a) Using undetermined coefficients.(b) Using variation of parameters.

Q: Solve using any method: y"+y' - 2y = sin x

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Q: b. (1+y²)y" + xy' - 3y = cos x solve and show that this equation is non- linear and non-homogeneous.…

A: As per the question we have to use the solution of the given second order differential equation to…

Q: (siny – 2ye*sinx)dx +(cosy + 2e*cosx)dy = 0

A: Given differential equation (sin y -2ye-x sinx ) dx+ (cosy+2e-x cos x ) dy=0

Q: Consider the equation below: u’=u2 – (7/x)u + 8/x2; u=-y’/y Obtain the linear second order…

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Q: Determine a suitable form for Y(t) if the method of undetermined coefficients is to be used. y" -…

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Q: Find the solution. dy sin x x +2y = y(2) = 1 dx , X A y = (4 + sin 2 + cosx²)/x² (B) cy= (3 cos 2x -…

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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.