87145 If \(m\) and \(n\) are respectively the order and the degree of the differential equation representing the family of curves \(y^{2}-5 a x-5 a^{\frac{3}{2}}=0(a>0\) is a parameter), then the value of \(m-n\) is

87146 If \(m\) and \(n\) are the order and degree of the differential equation of the family of parabolas with focus at the origin and \(\mathrm{X}\)-axis as its axis, then \(\mathbf{m n}-\mathbf{m}+\mathbf{n}=\)

87147 For the differential
\(\sqrt{\frac{d^{2} y}{d x^{2}}}=\sqrt[3]{\left[y \frac{d y}{d x}+x \sin \left(\frac{d y}{d x}\right)\right]^{2}}\)

87148 If \(\alpha\) and \(\beta\) are respectively the order and degree of the differential equation for which \(a x^{2}-b y^{2}=1\) is the general solution, then the eccentricity of the ellipse \(a x^{2}+b y^{2}=1\) is

87150 If the order and degree of the differential equation corresponding to the family of curves \((x-2)^{2}+(y-a)^{2}=b^{2}\), (where \(a\) and \(b\) are parameters) are \(m\) and \(n\) respectively, then \(\mathbf{m}^{2}+\mathbf{n}=\)

87145 If \(m\) and \(n\) are respectively the order and the degree of the differential equation representing the family of curves \(y^{2}-5 a x-5 a^{\frac{3}{2}}=0(a>0\) is a parameter), then the value of \(m-n\) is

87146 If \(m\) and \(n\) are the order and degree of the differential equation of the family of parabolas with focus at the origin and \(\mathrm{X}\)-axis as its axis, then \(\mathbf{m n}-\mathbf{m}+\mathbf{n}=\)

87147 For the differential
\(\sqrt{\frac{d^{2} y}{d x^{2}}}=\sqrt[3]{\left[y \frac{d y}{d x}+x \sin \left(\frac{d y}{d x}\right)\right]^{2}}\)

87148 If \(\alpha\) and \(\beta\) are respectively the order and degree of the differential equation for which \(a x^{2}-b y^{2}=1\) is the general solution, then the eccentricity of the ellipse \(a x^{2}+b y^{2}=1\) is

87150 If the order and degree of the differential equation corresponding to the family of curves \((x-2)^{2}+(y-a)^{2}=b^{2}\), (where \(a\) and \(b\) are parameters) are \(m\) and \(n\) respectively, then \(\mathbf{m}^{2}+\mathbf{n}=\)

87145 If \(m\) and \(n\) are respectively the order and the degree of the differential equation representing the family of curves \(y^{2}-5 a x-5 a^{\frac{3}{2}}=0(a>0\) is a parameter), then the value of \(m-n\) is

87146 If \(m\) and \(n\) are the order and degree of the differential equation of the family of parabolas with focus at the origin and \(\mathrm{X}\)-axis as its axis, then \(\mathbf{m n}-\mathbf{m}+\mathbf{n}=\)

87147 For the differential
\(\sqrt{\frac{d^{2} y}{d x^{2}}}=\sqrt[3]{\left[y \frac{d y}{d x}+x \sin \left(\frac{d y}{d x}\right)\right]^{2}}\)

87148 If \(\alpha\) and \(\beta\) are respectively the order and degree of the differential equation for which \(a x^{2}-b y^{2}=1\) is the general solution, then the eccentricity of the ellipse \(a x^{2}+b y^{2}=1\) is

87150 If the order and degree of the differential equation corresponding to the family of curves \((x-2)^{2}+(y-a)^{2}=b^{2}\), (where \(a\) and \(b\) are parameters) are \(m\) and \(n\) respectively, then \(\mathbf{m}^{2}+\mathbf{n}=\)

87145 If \(m\) and \(n\) are respectively the order and the degree of the differential equation representing the family of curves \(y^{2}-5 a x-5 a^{\frac{3}{2}}=0(a>0\) is a parameter), then the value of \(m-n\) is

87146 If \(m\) and \(n\) are the order and degree of the differential equation of the family of parabolas with focus at the origin and \(\mathrm{X}\)-axis as its axis, then \(\mathbf{m n}-\mathbf{m}+\mathbf{n}=\)

87147 For the differential
\(\sqrt{\frac{d^{2} y}{d x^{2}}}=\sqrt[3]{\left[y \frac{d y}{d x}+x \sin \left(\frac{d y}{d x}\right)\right]^{2}}\)

87148 If \(\alpha\) and \(\beta\) are respectively the order and degree of the differential equation for which \(a x^{2}-b y^{2}=1\) is the general solution, then the eccentricity of the ellipse \(a x^{2}+b y^{2}=1\) is

87150 If the order and degree of the differential equation corresponding to the family of curves \((x-2)^{2}+(y-a)^{2}=b^{2}\), (where \(a\) and \(b\) are parameters) are \(m\) and \(n\) respectively, then \(\mathbf{m}^{2}+\mathbf{n}=\)

87145 If \(m\) and \(n\) are respectively the order and the degree of the differential equation representing the family of curves \(y^{2}-5 a x-5 a^{\frac{3}{2}}=0(a>0\) is a parameter), then the value of \(m-n\) is

87146 If \(m\) and \(n\) are the order and degree of the differential equation of the family of parabolas with focus at the origin and \(\mathrm{X}\)-axis as its axis, then \(\mathbf{m n}-\mathbf{m}+\mathbf{n}=\)

87147 For the differential
\(\sqrt{\frac{d^{2} y}{d x^{2}}}=\sqrt[3]{\left[y \frac{d y}{d x}+x \sin \left(\frac{d y}{d x}\right)\right]^{2}}\)

87148 If \(\alpha\) and \(\beta\) are respectively the order and degree of the differential equation for which \(a x^{2}-b y^{2}=1\) is the general solution, then the eccentricity of the ellipse \(a x^{2}+b y^{2}=1\) is

87150 If the order and degree of the differential equation corresponding to the family of curves \((x-2)^{2}+(y-a)^{2}=b^{2}\), (where \(a\) and \(b\) are parameters) are \(m\) and \(n\) respectively, then \(\mathbf{m}^{2}+\mathbf{n}=\)