у`=e^(x^3)*(x^3)`=3x^2*e^(x^3)
y``=(3x^2)`*e^(x^3)+(3x^2)*(e^(x^3))`=6x*(e^(x^3))+3x^2*3x^2*e^(x^3)=
=(6x+9x^4)*e^(x^3)
y```=(6x+9x^4)`*e^(x^3)+(6x+9x^4)*(e^(x^3))`=
=(6+9*4x^3)`*e^(x^3)+(6x+9x^4)*(e^(x^3))*(3x^2)=
=(6+36x^3+18x^3+27x^6)*e^(x^3)=
=[b](6+54x^3+27x^6)*e^(x^3).[/b]
2
x`_(t)=e^(2t)*2
y`_(t)=e^(3t)*3
y`_(x)=[m]\frac{y`_{t}}{x`_{t}}=\frac{3e^{3t}}{2e^{2t}}=\frac{3}{2}e^{t}[/m]
y``_(xx)=[m]\frac{(y`_{x})`_{t}}{(x`_{t})`_{t}}=\frac{3}{2}\frac{e^{t}}{4e^{2t}}=\frac{3}{8e^{t}}[/m]
3.
(x^3+y^3-3axy)`=0
3x^2+3y^2*y`-3ay-3ax*y`=0
(3y^2-3ax)*y`=3ay-3x^2
y`=[m]\frac{3ay-3x^2}{3y^2-3ax}[/m]