ecuació diferencial

( y(x) )^{n}d_{xx}^{2}[y(x)] = f(x)

(1/(n+1))( y(x) )^{n+1} [o(x)o] d_{x}[y(x)] = int[f(x)] d[x] [o(x)o] y(x)

(1/(n+1))(1/(n+2))( y(x) )^{n+2} = ...

... int[ int[f(x)] d[x] ] d[x] [o(xx)o] int[y(x)] d[x]

y(x) / [o(xx)o] / ( int[y(x)] d[x] )^{(1/(n+2))} = ...

... ( (n+1)·(n+2)·int[ int[f(x)] d[x] ] d[x] )^{(1/(n+2))} 

( (n+2)/(n+1) )·( int[y(x)] d[x] )^{((n+1)/(n+2))} = ...

... int[ ( (n+1)·(n+2)·int[ int[f(x)] d[x] ] d[x] )^{(1/(n+2))} ] d[x]

 y(x) = ...

... d_{x}[ ( ( (n+1)/(n+2) )·int[ ( (n+1)·(n+2)·int[ int[f(x)] d[x] ] d[x] )^{(1/(n+2))} ] d[x] )^{((n+2)/(n+1))} ] 

y(x) = ...

... ( int[ ( (n+1)·(n+2)·int[ int[f(x)] d[x] ] d[x] )^{(1/(n+2))} ] d[x] )^{(1/(n+1))} [o(xx)o] ...

... ( (n+1)·(n+2)·int[ int[f(x)] d[x] ] d[x] )^{(1/(n+2))}

d_{x}[y(x)] = ...

... ( int[ ( (n+1)·(n+2)·int[ int[f(x)] d[x] ] d[x] )^{(1/(n+2))} ] d[x] )^{((-n)/(n+1))} [o(x)o] ...

... ( (n+1)·(n+2)·int[ int[f(x)] d[x] ] d[x] )^{((-n)/(n+2))} [o(x)o] (n+1)·int[f(x)] d[x]

 

( 1/y(x) )·d_{xx}^{2}[y(x)] = f(x)

ln[o(x)o](y(x)) [o(x)o] ln[o(x)o](d_{x}[y(x)]) = int[f(x)] d[x]

ln[o(x)o]( y(x) [o(x)o] d_{x}[y(x)] ) = int[f(x)] d[x]

y(x) [o(x)o] d_{x}[y(x)] = exp[o(x)o]( int[f(x)] d[x] )

y(x)  = ( 2·int[ exp[o(x)o]( int[f(x)] d[x] ) ] d[x] )^{(1/2)}

d_{x}[exp[o(x)o]( int[f(x)] d[x] ) / [o(x)o] / ( 2·int[ exp[o(x)o]( int[f(x)] d[x] ) ] d[x] )^{(-1)(1/2)}] = ...

... ( ( 2·int[ exp[o(x)o]( int[f(x)] d[x] ) ] d[x] )^{(1/2)}/exp[o(x)o]( int[f(x)] d[x] ) )·...

... exp[o(x)o]( int[f(x)] d[x] )·f(x) 

( 1/( y(x) )^{2} )·d_{xx}^{2}[y(x)] = f(x)

(-1)·( 1/( y(x) ) ) [o(x)o] d_{x}[y(x)] = int[f(x)] d[x] [o(x)o] y(x)

(-1)·ln[o(xx)o](y(x)) = int[ int[f(x)] d[x] ] d[x] [o(xx)o] int[y(x)] d[x]

exp[o(xx)o]( int[y(x)] d[x] ) [o(xx)o] ( y(x) ) = exp[o(xx)o]( (-1)·int[ int[f(x)] d[x] ] d[x] )

exp[o(xx)o]( int[y(x)] d[x] ) = int[ exp[o(xx)o]( (-1)·int[ int[f(x)] d[x] ] d[x] ) ] d[x] 

y(x) = ( int[ exp[o(xx)o]( (-1)·int[ int[f(x)] d[x] ] d[x] ) ] d[x] )^{(-1)} [o(xx)o]·...

... exp[o(xx)o]( (-1)·int[ int[f(x)] d[x] ] d[x] )

d_{x}[y(x)] = ( int[ exp[o(xx)o]( (-1)·int[ int[f(x)] d[x] ] d[x] ) ] d[x] )^{(-2)} [o(x)o]...

... exp[o(xx)o]( (-2)·int[ int[f(x)] d[x] ] d[x] ) [o(x)o] int[f(x)] d[x]