Consider the differential equation: -35t2y''+14t(t+5)y'-14(t+5)y=0, t>0. a. Given that y1(t)=5t is a solution, apply the reduction of order method to find another solution y2 for wich y1 and y2 form a fundamental solution set.  i. Starting with y1, solve for w in y1w'+(2y'1+p(t)y1)w=0 so that w(1)=-2 ii. Now solve for u'=w so that u(1)=3. iii. Finially, write down y2 using the u that you found b. Find the particular solution corresponding to the initial conditions y(1)=-5 and y'(1)=0

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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.