Using the method of variation of parameters, solve the following inhomogeneous equation. y′′+12y′+36y=(−1e−6x)/(x2+1) a) Write the characteristic equation of the homogeneous part of the equation using the variable m. ....?....=0 b) Write down the homogeneous solution of the equation. Denote the constants c1 and c2 with c1 and c2. The y1 and y2 solutions must satisfy the conditions y1(0)=1, y2(0)=0, respectively. yh=? c) Find Wronskian: W(y1,y2)=?

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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.