87293 Find the solution of the differential equation \(\left(\mathbf{e}^{\mathbf{y}-\mathbf{x}}\right) \mathbf{d} \mathbf{y}=\left(\mathrm{e}^{\mathbf{x}}-\mathbf{e}^{\mathbf{y}}\right) \mathbf{d x}\)

87277 Let \(y=y(x)\) be the solution of the differential equation \(\left(3 y^{2}-5 x^{2}\right) y d x+2 x\left(x^{2}-y^{2}\right) d y=0\) such that \(\mathbf{y}(1)=1\). Then \(\left|(\mathbf{y}(\mathbf{2}))^{3}-12 \mathrm{y}(2)\right|\) is equal to:

87278 The general solution of the differential equation \(\left(x-y^{2}\right) d x+y\left(5 x+y^{2}\right) d y=0\) is :

87279 If the solution curve \(y=y(x)\) of the differential equation \(y^{2} d x+\left(x^{2}-x y+y^{2}\right) d y=0\), which passes through the point \((1,1)\) and intersects the line \(y=\sqrt{3} x\) at the point \((\alpha, \sqrt{3} \alpha)\), then value of \(\log _{e}(\sqrt{3} \alpha)\) is equal to

87293 Find the solution of the differential equation \(\left(\mathbf{e}^{\mathbf{y}-\mathbf{x}}\right) \mathbf{d} \mathbf{y}=\left(\mathrm{e}^{\mathbf{x}}-\mathbf{e}^{\mathbf{y}}\right) \mathbf{d x}\)

87277 Let \(y=y(x)\) be the solution of the differential equation \(\left(3 y^{2}-5 x^{2}\right) y d x+2 x\left(x^{2}-y^{2}\right) d y=0\) such that \(\mathbf{y}(1)=1\). Then \(\left|(\mathbf{y}(\mathbf{2}))^{3}-12 \mathrm{y}(2)\right|\) is equal to:

87278 The general solution of the differential equation \(\left(x-y^{2}\right) d x+y\left(5 x+y^{2}\right) d y=0\) is :

87279 If the solution curve \(y=y(x)\) of the differential equation \(y^{2} d x+\left(x^{2}-x y+y^{2}\right) d y=0\), which passes through the point \((1,1)\) and intersects the line \(y=\sqrt{3} x\) at the point \((\alpha, \sqrt{3} \alpha)\), then value of \(\log _{e}(\sqrt{3} \alpha)\) is equal to

87293 Find the solution of the differential equation \(\left(\mathbf{e}^{\mathbf{y}-\mathbf{x}}\right) \mathbf{d} \mathbf{y}=\left(\mathrm{e}^{\mathbf{x}}-\mathbf{e}^{\mathbf{y}}\right) \mathbf{d x}\)

87277 Let \(y=y(x)\) be the solution of the differential equation \(\left(3 y^{2}-5 x^{2}\right) y d x+2 x\left(x^{2}-y^{2}\right) d y=0\) such that \(\mathbf{y}(1)=1\). Then \(\left|(\mathbf{y}(\mathbf{2}))^{3}-12 \mathrm{y}(2)\right|\) is equal to:

87278 The general solution of the differential equation \(\left(x-y^{2}\right) d x+y\left(5 x+y^{2}\right) d y=0\) is :

87279 If the solution curve \(y=y(x)\) of the differential equation \(y^{2} d x+\left(x^{2}-x y+y^{2}\right) d y=0\), which passes through the point \((1,1)\) and intersects the line \(y=\sqrt{3} x\) at the point \((\alpha, \sqrt{3} \alpha)\), then value of \(\log _{e}(\sqrt{3} \alpha)\) is equal to

87293 Find the solution of the differential equation \(\left(\mathbf{e}^{\mathbf{y}-\mathbf{x}}\right) \mathbf{d} \mathbf{y}=\left(\mathrm{e}^{\mathbf{x}}-\mathbf{e}^{\mathbf{y}}\right) \mathbf{d x}\)

87277 Let \(y=y(x)\) be the solution of the differential equation \(\left(3 y^{2}-5 x^{2}\right) y d x+2 x\left(x^{2}-y^{2}\right) d y=0\) such that \(\mathbf{y}(1)=1\). Then \(\left|(\mathbf{y}(\mathbf{2}))^{3}-12 \mathrm{y}(2)\right|\) is equal to:

87278 The general solution of the differential equation \(\left(x-y^{2}\right) d x+y\left(5 x+y^{2}\right) d y=0\) is :

87279 If the solution curve \(y=y(x)\) of the differential equation \(y^{2} d x+\left(x^{2}-x y+y^{2}\right) d y=0\), which passes through the point \((1,1)\) and intersects the line \(y=\sqrt{3} x\) at the point \((\alpha, \sqrt{3} \alpha)\), then value of \(\log _{e}(\sqrt{3} \alpha)\) is equal to