Y'=y/x-ctg(y/x) Решите дифференциальные уравнения Solve the following differential equations

[latex]y'=\frac{y}{x}-ctg(\frac{y}{x})[/latex] [latex]\frac{y}{x}=t[/latex] [latex]y=tx[/latex] [latex]y'=t'x+t[/latex] [latex]t'x+t=t-ctg t[/latex] [latex] \frac{dt}{dx} x=-ctg t[/latex] [latex] \frac{dt}{ctg t} =- \frac{dx}{x} [/latex] [latex] \frac{sint dt}{cost}= - \frac{dx}{x}[/latex] [latex]-\frac{d(cost)}{cost}= - \frac{dx}{x}[/latex] [latex]ln cos t=lnx+C[/latex] [latex]cost=Cx[/latex] [latex]t=arccos(Cx)[/latex] [latex]\frac{y}{x}=arccos(Cx)[/latex] [latex]y=x*arccos(Cx)[/latex]