Class 12 Math Calculus Differential Equations

The number of arbitrary constants in the general solution of a differential equationof fourth order are:(A) 0 (B) 2 (C) 3 (D) 4

Solution: Solution: General equation of 4th order is

$dx_{4}d_{4}y =k$$dx_{3}d_{3}y =kx+c1$

$dx_{2}d_{2}y =k2x_{2} +c1x+c2$

$dxdy =k6x_{3} +(c1)2x_{2} +c2x+c3$

$y=k24x_{4} +(c1)6x_{3} +c22x_{2} +c3x+c4$

Number of arbitrary constant=$4$

$dx_{4}d_{4}y =k$$dx_{3}d_{3}y =kx+c1$

$dx_{2}d_{2}y =k2x_{2} +c1x+c2$

$dxdy =k6x_{3} +(c1)2x_{2} +c2x+c3$

$y=k24x_{4} +(c1)6x_{3} +c22x_{2} +c3x+c4$

Number of arbitrary constant=$4$

Similar topics

relations and functions

integrals

trigonometric functions

inverse trigonometric functions

application of derivatives

relations and functions

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