87091
The order of the differential equation \(2 x^{2} \frac{d^{2} y}{d x^{2}}-3 \frac{d y}{d x}+y=0\)
1 2
2 1
3 0
4 not defined
Explanation:
(A) : The differential equation \(2 x^{2} \frac{d^{2} y}{d x^{2}}-3 \frac{d y}{d x}+y=0\) Order is 2 and degree is 1
SRM JEEE-2018
Differential Equation
87093
The order of the differential equation of all circles of radius ' \(r\) ', having center on \(\mathbf{y}\)-axis and passing through the origin is
1 1
2 2
3 3
4 4
Explanation:
(A) : The equation of a family of circle of radius \(r\) passing through the origin and having center on \(\mathrm{y}-\) axis is \((x-0)^{2}+(y-r)^{2}=r^{2}\) or \(x^{2}+y^{2}-2 r y=0\) So, this is one parameter family of circle, so its differential equation is order one.
SRM JEEE-2010
Differential Equation
87097
The general solution of \(x^{2} \frac{d y}{d x}=2\) is-
1 \(y=c+\frac{2}{x}\)
2 \(y=c-\frac{2}{x}\)
3 \(y=2 c x\)
4 \(y=c-\frac{3}{x^{3}}\)
Explanation:
(B) : Given, \(\frac{d y}{d x}=\frac{2}{x^{2}} \Rightarrow \quad d y=\frac{2}{x^{2}} d x\) Integrate both side, we get- \(y=-\frac{2}{x}+c\)
BITSAT-2007
Differential Equation
87100
Order and degree of the differential equation \(\frac{d^{4} y}{d^{4}}+\sin \left(\frac{d^{3} y}{d^{3}}\right)=0\)
1 order \(=4\), degree \(=1\)
2 order \(=3\), degree \(=1\)
3 order \(=4\), degree \(=\) not defined
4 order \(=4\), degree \(=2\)
Explanation:
(C) : Given, \(\frac{d^{4} y}{d x^{4}}+\sin \left(\frac{d^{3} y}{d x^{3}}\right)=0\) The highest order derivative which occurs in the given differential equation is \(\frac{d^{4} y}{d x^{4}}\), therefore its order is 4 . As the given differential equation is not a polynomial equation is \(\frac{\mathrm{dy}}{\mathrm{dx}}\), therefore its degree is not defined.
87091
The order of the differential equation \(2 x^{2} \frac{d^{2} y}{d x^{2}}-3 \frac{d y}{d x}+y=0\)
1 2
2 1
3 0
4 not defined
Explanation:
(A) : The differential equation \(2 x^{2} \frac{d^{2} y}{d x^{2}}-3 \frac{d y}{d x}+y=0\) Order is 2 and degree is 1
SRM JEEE-2018
Differential Equation
87093
The order of the differential equation of all circles of radius ' \(r\) ', having center on \(\mathbf{y}\)-axis and passing through the origin is
1 1
2 2
3 3
4 4
Explanation:
(A) : The equation of a family of circle of radius \(r\) passing through the origin and having center on \(\mathrm{y}-\) axis is \((x-0)^{2}+(y-r)^{2}=r^{2}\) or \(x^{2}+y^{2}-2 r y=0\) So, this is one parameter family of circle, so its differential equation is order one.
SRM JEEE-2010
Differential Equation
87097
The general solution of \(x^{2} \frac{d y}{d x}=2\) is-
1 \(y=c+\frac{2}{x}\)
2 \(y=c-\frac{2}{x}\)
3 \(y=2 c x\)
4 \(y=c-\frac{3}{x^{3}}\)
Explanation:
(B) : Given, \(\frac{d y}{d x}=\frac{2}{x^{2}} \Rightarrow \quad d y=\frac{2}{x^{2}} d x\) Integrate both side, we get- \(y=-\frac{2}{x}+c\)
BITSAT-2007
Differential Equation
87100
Order and degree of the differential equation \(\frac{d^{4} y}{d^{4}}+\sin \left(\frac{d^{3} y}{d^{3}}\right)=0\)
1 order \(=4\), degree \(=1\)
2 order \(=3\), degree \(=1\)
3 order \(=4\), degree \(=\) not defined
4 order \(=4\), degree \(=2\)
Explanation:
(C) : Given, \(\frac{d^{4} y}{d x^{4}}+\sin \left(\frac{d^{3} y}{d x^{3}}\right)=0\) The highest order derivative which occurs in the given differential equation is \(\frac{d^{4} y}{d x^{4}}\), therefore its order is 4 . As the given differential equation is not a polynomial equation is \(\frac{\mathrm{dy}}{\mathrm{dx}}\), therefore its degree is not defined.
NEET Test Series from KOTA - 10 Papers In MS WORD
WhatsApp Here
Differential Equation
87091
The order of the differential equation \(2 x^{2} \frac{d^{2} y}{d x^{2}}-3 \frac{d y}{d x}+y=0\)
1 2
2 1
3 0
4 not defined
Explanation:
(A) : The differential equation \(2 x^{2} \frac{d^{2} y}{d x^{2}}-3 \frac{d y}{d x}+y=0\) Order is 2 and degree is 1
SRM JEEE-2018
Differential Equation
87093
The order of the differential equation of all circles of radius ' \(r\) ', having center on \(\mathbf{y}\)-axis and passing through the origin is
1 1
2 2
3 3
4 4
Explanation:
(A) : The equation of a family of circle of radius \(r\) passing through the origin and having center on \(\mathrm{y}-\) axis is \((x-0)^{2}+(y-r)^{2}=r^{2}\) or \(x^{2}+y^{2}-2 r y=0\) So, this is one parameter family of circle, so its differential equation is order one.
SRM JEEE-2010
Differential Equation
87097
The general solution of \(x^{2} \frac{d y}{d x}=2\) is-
1 \(y=c+\frac{2}{x}\)
2 \(y=c-\frac{2}{x}\)
3 \(y=2 c x\)
4 \(y=c-\frac{3}{x^{3}}\)
Explanation:
(B) : Given, \(\frac{d y}{d x}=\frac{2}{x^{2}} \Rightarrow \quad d y=\frac{2}{x^{2}} d x\) Integrate both side, we get- \(y=-\frac{2}{x}+c\)
BITSAT-2007
Differential Equation
87100
Order and degree of the differential equation \(\frac{d^{4} y}{d^{4}}+\sin \left(\frac{d^{3} y}{d^{3}}\right)=0\)
1 order \(=4\), degree \(=1\)
2 order \(=3\), degree \(=1\)
3 order \(=4\), degree \(=\) not defined
4 order \(=4\), degree \(=2\)
Explanation:
(C) : Given, \(\frac{d^{4} y}{d x^{4}}+\sin \left(\frac{d^{3} y}{d x^{3}}\right)=0\) The highest order derivative which occurs in the given differential equation is \(\frac{d^{4} y}{d x^{4}}\), therefore its order is 4 . As the given differential equation is not a polynomial equation is \(\frac{\mathrm{dy}}{\mathrm{dx}}\), therefore its degree is not defined.
87091
The order of the differential equation \(2 x^{2} \frac{d^{2} y}{d x^{2}}-3 \frac{d y}{d x}+y=0\)
1 2
2 1
3 0
4 not defined
Explanation:
(A) : The differential equation \(2 x^{2} \frac{d^{2} y}{d x^{2}}-3 \frac{d y}{d x}+y=0\) Order is 2 and degree is 1
SRM JEEE-2018
Differential Equation
87093
The order of the differential equation of all circles of radius ' \(r\) ', having center on \(\mathbf{y}\)-axis and passing through the origin is
1 1
2 2
3 3
4 4
Explanation:
(A) : The equation of a family of circle of radius \(r\) passing through the origin and having center on \(\mathrm{y}-\) axis is \((x-0)^{2}+(y-r)^{2}=r^{2}\) or \(x^{2}+y^{2}-2 r y=0\) So, this is one parameter family of circle, so its differential equation is order one.
SRM JEEE-2010
Differential Equation
87097
The general solution of \(x^{2} \frac{d y}{d x}=2\) is-
1 \(y=c+\frac{2}{x}\)
2 \(y=c-\frac{2}{x}\)
3 \(y=2 c x\)
4 \(y=c-\frac{3}{x^{3}}\)
Explanation:
(B) : Given, \(\frac{d y}{d x}=\frac{2}{x^{2}} \Rightarrow \quad d y=\frac{2}{x^{2}} d x\) Integrate both side, we get- \(y=-\frac{2}{x}+c\)
BITSAT-2007
Differential Equation
87100
Order and degree of the differential equation \(\frac{d^{4} y}{d^{4}}+\sin \left(\frac{d^{3} y}{d^{3}}\right)=0\)
1 order \(=4\), degree \(=1\)
2 order \(=3\), degree \(=1\)
3 order \(=4\), degree \(=\) not defined
4 order \(=4\), degree \(=2\)
Explanation:
(C) : Given, \(\frac{d^{4} y}{d x^{4}}+\sin \left(\frac{d^{3} y}{d x^{3}}\right)=0\) The highest order derivative which occurs in the given differential equation is \(\frac{d^{4} y}{d x^{4}}\), therefore its order is 4 . As the given differential equation is not a polynomial equation is \(\frac{\mathrm{dy}}{\mathrm{dx}}\), therefore its degree is not defined.