Consider the differential equation: (56x^2)y″−16x(x+7)y′+16(x+7)y=5x3, x>0.   You can verify that y1=2x and y2=5xexp⁡(2x/7) satisfy the corresponding homogeneous equation.   Compute the Wronskian W between y1 and y2 Apply variation of parameters to find a particular solution.

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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.