jee-main 2014 Q86

jee-main · India · 09apr Differential equations Higher-Order and Special DEs (Proof/Theory)

If the differential equation representing the family of all circles touching $x$-axis at the origin is $\left( x ^ { 2 } - y ^ { 2 } \right) \frac { d y } { d x } = g ( x ) y$, then $g ( x )$ equals
(1) $\frac { 1 } { 2 } x ^ { 2 }$
(2) $2 x$
(3) $\frac { 1 } { 2 } x$
(4) $2 x ^ { 2 }$

If the differential equation representing the family of all circles touching $x$-axis at the origin is $\left( x ^ { 2 } - y ^ { 2 } \right) \frac { d y } { d x } = g ( x ) y$, then $g ( x )$ equals\\
(1) $\frac { 1 } { 2 } x ^ { 2 }$\\
(2) $2 x$\\
(3) $\frac { 1 } { 2 } x$\\
(4) $2 x ^ { 2 }$

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