x2y + 3xy – xy – 3y.
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A prefix is a group of letters placed before the root of a word. For example, the word “unhappy” consists of the prefix “un-” [which means “not”] combined with the root (or stem) word “happy”; the word “unhappy” means “not happy.”
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Hint: This is Euler-Cauchy type equation, so let:
y=xm⟹y′=mxm−1⟹y′′=m(m−1)xm−2
Substitute back into ODE, solve for roots, write the general solution and then find constants from initial conditions
y ( ×)=× ( × ^2 +3).
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