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Differential Equation

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

1 \(e^{y} e^{x}=e^{2 x}-e^{x 2}+c\)
2 \(e^{y} e^{x}=e^{x} e^{e^{x}}-e^{e^{y}}+c\)
3 \(e^{y} e^{e^{x}}=e^{x} e^{e^{x}}-e^{e^{x}}+c\)
4 \(e^{e^{y}} e^{x}=e^{x} e^{e^{x}}-e^{e^{x}}+c\)
AP EAMCET-17.09.2020
Differential Equation

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:

1 64
2 \(32 \sqrt{2}\)
3 32
4 \(16 \sqrt{2}\)
JEE Main-31.01.2023
Differential Equation

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 :

1 \(\left(y^{2}+x\right)^{4}=C \mid\left(y^{2}+2 x\right)^{3}\)
2 \(\left(y^{2}+2 x\right)^{4}=C\left|\left(y^{2}+x\right)^{3}\right|\)
3 \(\left|\left(y^{2}+x\right)^{3}\right|=C\left(2 y^{2}+x\right)^{4}\)
4 \(\left|\left(y^{2}+2 x\right)^{3}\right|=C\left(2 y^{2}+x\right)^{4}\)
JEE Main-25.07.2022
Differential Equation

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

1 \(\frac{\pi}{3}\)
2 \(\frac{\pi}{2}\)
3 \(\frac{\pi}{12}\)
4 \(\frac{\pi}{6}\)
JEE Main-25.06.2022
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Differential Equation

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

1 \(e^{y} e^{x}=e^{2 x}-e^{x 2}+c\)
2 \(e^{y} e^{x}=e^{x} e^{e^{x}}-e^{e^{y}}+c\)
3 \(e^{y} e^{e^{x}}=e^{x} e^{e^{x}}-e^{e^{x}}+c\)
4 \(e^{e^{y}} e^{x}=e^{x} e^{e^{x}}-e^{e^{x}}+c\)
AP EAMCET-17.09.2020
Differential Equation

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:

1 64
2 \(32 \sqrt{2}\)
3 32
4 \(16 \sqrt{2}\)
JEE Main-31.01.2023
Differential Equation

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 :

1 \(\left(y^{2}+x\right)^{4}=C \mid\left(y^{2}+2 x\right)^{3}\)
2 \(\left(y^{2}+2 x\right)^{4}=C\left|\left(y^{2}+x\right)^{3}\right|\)
3 \(\left|\left(y^{2}+x\right)^{3}\right|=C\left(2 y^{2}+x\right)^{4}\)
4 \(\left|\left(y^{2}+2 x\right)^{3}\right|=C\left(2 y^{2}+x\right)^{4}\)
JEE Main-25.07.2022
Differential Equation

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

1 \(\frac{\pi}{3}\)
2 \(\frac{\pi}{2}\)
3 \(\frac{\pi}{12}\)
4 \(\frac{\pi}{6}\)
JEE Main-25.06.2022
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NEET Test Series from KOTA - 10 Papers In MS WORD WhatsApp Here
Differential Equation

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

1 \(e^{y} e^{x}=e^{2 x}-e^{x 2}+c\)
2 \(e^{y} e^{x}=e^{x} e^{e^{x}}-e^{e^{y}}+c\)
3 \(e^{y} e^{e^{x}}=e^{x} e^{e^{x}}-e^{e^{x}}+c\)
4 \(e^{e^{y}} e^{x}=e^{x} e^{e^{x}}-e^{e^{x}}+c\)
AP EAMCET-17.09.2020
Differential Equation

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:

1 64
2 \(32 \sqrt{2}\)
3 32
4 \(16 \sqrt{2}\)
JEE Main-31.01.2023
Differential Equation

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 :

1 \(\left(y^{2}+x\right)^{4}=C \mid\left(y^{2}+2 x\right)^{3}\)
2 \(\left(y^{2}+2 x\right)^{4}=C\left|\left(y^{2}+x\right)^{3}\right|\)
3 \(\left|\left(y^{2}+x\right)^{3}\right|=C\left(2 y^{2}+x\right)^{4}\)
4 \(\left|\left(y^{2}+2 x\right)^{3}\right|=C\left(2 y^{2}+x\right)^{4}\)
JEE Main-25.07.2022
Differential Equation

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

1 \(\frac{\pi}{3}\)
2 \(\frac{\pi}{2}\)
3 \(\frac{\pi}{12}\)
4 \(\frac{\pi}{6}\)
JEE Main-25.06.2022
NEET DIGITAL LIBRARY
Differential Equation

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

1 \(e^{y} e^{x}=e^{2 x}-e^{x 2}+c\)
2 \(e^{y} e^{x}=e^{x} e^{e^{x}}-e^{e^{y}}+c\)
3 \(e^{y} e^{e^{x}}=e^{x} e^{e^{x}}-e^{e^{x}}+c\)
4 \(e^{e^{y}} e^{x}=e^{x} e^{e^{x}}-e^{e^{x}}+c\)
AP EAMCET-17.09.2020
Differential Equation

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:

1 64
2 \(32 \sqrt{2}\)
3 32
4 \(16 \sqrt{2}\)
JEE Main-31.01.2023
Differential Equation

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 :

1 \(\left(y^{2}+x\right)^{4}=C \mid\left(y^{2}+2 x\right)^{3}\)
2 \(\left(y^{2}+2 x\right)^{4}=C\left|\left(y^{2}+x\right)^{3}\right|\)
3 \(\left|\left(y^{2}+x\right)^{3}\right|=C\left(2 y^{2}+x\right)^{4}\)
4 \(\left|\left(y^{2}+2 x\right)^{3}\right|=C\left(2 y^{2}+x\right)^{4}\)
JEE Main-25.07.2022
Differential Equation

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

1 \(\frac{\pi}{3}\)
2 \(\frac{\pi}{2}\)
3 \(\frac{\pi}{12}\)
4 \(\frac{\pi}{6}\)
JEE Main-25.06.2022
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