Chapter 13: Problem 1104
The differential equation of all conics having centre at the origin is of order. (A) 2 (B) 3 (C) 4 (D) 5
Chapter 13: Problem 1104
The differential equation of all conics having centre at the origin is of order. (A) 2 (B) 3 (C) 4 (D) 5
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Get started for freeThe solution of \(\mathrm{x}^{2} \mathrm{y}-\mathrm{x}^{3}(\mathrm{dy} / \mathrm{dx})=\mathrm{y}^{4} \cos \mathrm{x} ; \mathrm{y}(0)=1\) is: (A) \(x^{3}=y^{3} \sin x\) (B) \(x^{3}=3 y^{3} \sin x\) (C) \(y^{3}=3 x^{3} \sin x\) (D) none the these
The solution of \((\mathrm{dy} / \mathrm{dx})=4 \mathrm{x}+\mathrm{y}+1 \mathrm{is}:\) (A) \(4 \mathrm{x}+\mathrm{y}+1=\mathrm{c} \cdot \mathrm{e}^{\mathrm{x}}\) (B) \(4 \mathrm{x}+\mathrm{y}+5=\mathrm{e}^{\mathrm{x}}+\mathrm{c}\) (C) \(4 \mathrm{x}+\mathrm{y}+5=\mathrm{c} \cdot \mathrm{e}^{\mathrm{x}}\) (D) none of these
\((\mathrm{dy} / \mathrm{dx})=\mathrm{e}^{\mathrm{x}+\mathrm{y}}+\mathrm{x}^{2} \mathrm{e}^{\mathrm{y}}\) has the particular solution for \(\mathrm{x}=\mathrm{y}\) \(=0:\) (A) \(\mathrm{e}^{\mathrm{x}}-\mathrm{e}^{-\mathrm{y}}+\left(\mathrm{x}^{3} / 3\right)=2\) (B) \(\mathrm{e}^{\mathrm{x}}+\mathrm{e}^{-\mathrm{y}}+\left(\mathrm{x}^{3} / 3\right)=2\) (C) \(\mathrm{e}^{\mathrm{x}-\mathrm{y}}+\left(\mathrm{x}^{3} / 3\right)=2\) (D) \(e^{y-x}-\left(x^{3} / 3\right)=2\)
The differential equation of family of circles of radius 'a' is: (A) \(a^{2} y_{2}=\left[1-y_{1}^{3}\right]^{2}\) (B) \(a^{2} y_{2}=\left[1-y_{1}^{2}\right]^{3}\) (C) \(a^{2}\left(y_{2}\right)^{2}=\left[1+y_{1}^{3}\right]^{2}\) (D) \(a^{2}\left(y_{2}\right)^{2}=\left[1+y_{1}^{2}\right]^{3}\)
Solution of the differential equation \(\cos \mathrm{x} \cdot \mathrm{dy}\)
\(=y(\sin x-y) d x, 0
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