ecuacions diferencials

y(x)·d_{x}[y(x)] = ax^{m}

y(x) = a^{(1/2)}·( 2/(m+1) )^{(1/2)}·x^{(m/2)+(1/2)}

y(x)·d_{x}[y(x)]·d_{xx}^{2}[y(x)] = ax^{m}

y(x) = a^{(1/3)}·( 3/(m+3) )^{(2/3)}·( 3/m )^{(1/3)}·x^{(m/3)+1}

y(x)·d_{x}[y(x)]·d_{xx}^{2}[y(x)]·d_{xxx}^{3}[y(x)] = ax^{m}

y(x) = a^{(1/4)}·( 4/(m+6) )^{(3/4)}·( 4/(m+2) )^{(1/2)}·( 4/(m+(-2)) )^{(1/4)}·x^{(m/4)+(3/2)}

y(x)·d_{xx}^{2}[y(x)] = ax^{m}

y(x) = a^{(1/2)}·( 2/(m+2) )^{(1/2)}·( 2/m )^{(1/2)}·x^{(m/2)+1}

y(x)·d_{xxx}^{3}[y(x)] = ax^{m}

y(x) = a^{(1/2)}·( 2/(m+3) )^{(1/2)}·( 2/(m+1) )^{(1/2)}·( 2/(m+(-1)) )^{(1/2)}·x^{(m/2)+(3/2)}