Find a particular solution of

x2y′′−7xy′+7y=13x12\displaystyle {x}^{{2}}{y}{''}-{7}{x}{y}'+{7}{y}={13}{x}^{{\frac{{1}}{{2}}}}

Hint: Write yp(x)=Ax12\displaystyle {y}_{{p}}{\left({x}\right)}={A}{x}^{{\frac{{1}}{{2}}}} and find A\displaystyle {A}
yp(x)=\displaystyle {y}_{{p}}{\left({x}\right)}=  

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