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Explore popular questions from Differential Equations for JEE Advanced. This collection covers Differential Equations previous year JEE Advanced questions hand picked by experienced teachers.

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Q 1. A solution of the differential equation {tex} \left( \frac { d y } { d x } \right) ^ { 2 } - x \frac { d y } { d x } + y = 0 {/tex} is
{tex} y = \left( C _ { 1 } + C _ { 2 } \right) \cos \left( x + C _ { 3 } \right) - C _ { 4 } e ^ { x + C _ { 5 } } , {/tex} where {tex} C _ { 1 } , C _ { 2 } , C _ { 3 } , C _ { 4 } {/tex} {tex} C _ { 5 } , {/tex} are arbitrary constants, is

A

{tex} y = 2 {/tex}

B

{tex} y = 2 x {/tex}

{tex} y = 2 x - 4 {/tex}

D

{tex} y = 2 x ^ { 2 } - 4 {/tex}

Explanation

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Q 2. If {tex} y = y ( x ) {/tex} and it follows the relation {tex} x \cos y + y \cos x = \pi {/tex} then {tex} y ^ {\prime\prime } ( 0 ) = {/tex}

A

{tex}1{/tex}

B

{tex} - 1 {/tex}

{tex} \pi - 1 {/tex}

D

{tex} - \pi {/tex}

Explanation


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Q 3. The solution of primitive integral equation {tex} \left( x ^ { 2 } + y ^ { 2 } \right) d y = x y {/tex} {tex} d x {/tex} is {tex} y = y ( x ) {/tex}. If {tex} y ( 1 ) = 1 {/tex} and {tex} \left( x _ { 0 } \right) = e , {/tex} then {tex} x _ { 0 } {/tex} is equal to

A

{tex} \sqrt { 2 \left( e ^ { 2 } - 1 \right) } {/tex}

B

{tex} \sqrt { 2 \left( e ^ { 2 } + 1 \right) } {/tex}

{tex} \sqrt { 3 } e {/tex}

D

{tex} \sqrt { \frac { e ^ { 2 } + 1 } { 2 } } {/tex}

Explanation


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Q 4. The differential equation {tex} \frac { d y } { d x } = \frac { \sqrt { 1 - y ^ { 2 } } } { y } {/tex} determines a family of circles with

A

variable radii and a fixed centre at {tex} ( 0,1 ) {/tex}

B

variable radii and a fixed centre at {tex} ( 0 , - 1 ) {/tex}

fixed radius {tex}1{/tex} and variable centres along the x-axis.

D

fixed radius {tex}1{/tex} and variable centres along the {tex} y {/tex} -axis.

Explanation


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Q 5. The differential equation of the system of circles touching the {tex} x {/tex} -axis at origin is

A

{tex} \left( x ^ { 2 } - y ^ { 2 } \right) \frac { d y } { d x } - 2 x y = 0 {/tex}

{tex} \left( x ^ { 2 } - y ^ { 2 } \right) \frac { d y } { d x } + 2 x y = 0 {/tex}

C

{tex} \left( x ^ { 2 } + y ^ { 2 } \right) \frac { d y } { d x } - 2 x y = 0 {/tex}

D

{tex} \left( x ^ { 2 } + y ^ { 2 } \right) \frac { d y } { d x } + 2 x y = 0 {/tex}

Explanation