y'=z'x+z\right]\\ x(z'x+z)=zx*sin^2lnz\\ z'x=z*sin^2lnz-z\\ \int\dfrac{dz}{z*(-cos^2lnz)}=\int\dfrac{dx}{x}\\ -\int\dfrac{d(lnz)}{cos^2lnz}=\int\dfrac{dx}{x}\\ -tg(lnz)=ln(Cx)\\ -tg(ln\dfrac{y}{x})=ln(Cx)\\ y(1)=1=>-tg(ln1)=ln(C)=>C=1=>\\ tg(ln\dfrac{y}{x})=-ln(x)" alt="xy'=y*sin^2ln\dfrac{y}{x}\\ \left[y=zx=>y'=z'x+z\right]\\ x(z'x+z)=zx*sin^2lnz\\ z'x=z*sin^2lnz-z\\ \int\dfrac{dz}{z*(-cos^2lnz)}=\int\dfrac{dx}{x}\\ -\int\dfrac{d(lnz)}{cos^2lnz}=\int\dfrac{dx}{x}\\ -tg(lnz)=ln(Cx)\\ -tg(ln\dfrac{y}{x})=ln(Cx)\\ y(1)=1=>-tg(ln1)=ln(C)=>C=1=>\\ tg(ln\dfrac{y}{x})=-ln(x)" align="absmiddle" class="latex-formula">