Q-40- The order of the differential equation whose general solution is given by y-c1-c2 -160-cosx-c3-c4 -160-ex-C5 where c1- -160-c2- -160-c3- -160-c4- -160-c5 are arbitrary constants is-A- 5-B- 4-C- 3-D- 2

Order #160;of #160;differential #160;equation=Number #160;of #160;independent #160;arbitary #160;constanty=c1+c2 #160;cos #160;x+c3 c4ex+c5y=c ...

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Standard XII

Mathematics

Ordinary Differential Equations

Q.40. The ord...

Question

Q.40. The order of the differential equation whose general solution is given by $y = (c_{1} + c_{2}) \cos (x + c_{3}) - c_{4} e^{x + C_{5}}$ where $c_{1}, c_{2}, c_{3}, c_{4}, c_{5}$ are arbitrary constants is
A) 5
B) 4
C) 3
D) 2

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Solution

$O r d e r o f d i f f e r e n t i a l e q u a t i o n = N u m b e r o f i n d e p e n d e n t a r b i t a r y c o n s \tan t y = (c_{1} + c_{2}) \cos (x + c_{3}) - c_{4} e^{x + c_{5}} y = (c_{1} + c_{2}) \cos (x + c_{3}) - c_{4} e^{c_{5}} . e^{x} P u t c_{1} + c_{2} = c a n d c_{4} e^{c_{5}} = k y = c \cos (x + c_{3}) - k e^{x} H e n c e t h e r e a r e o n l y 3 i n d e p e n d e n t a r b i t a r y c o n s \tan t s H e n c e o r d e r o f d i f f e r e n t i a l e q u a t i o n = 3$

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Q.40. The order of the differential equation whose general solution is given by y=c1+c2 cosx+c3-c4 ex+C5 where c1, c2, c3, c4, c5 are arbitrary constants is A) 5 B) 4 C) 3 D) 2

Order of differential equation=Number of independent arbitary constanty=c1+c2 cos x+c3-c4ex+c5y=c1+c2 cos x+c3-c4ec5.exPut c1+c2=c and c4ec5=ky=c cos x+c3-kexHence there are only 3 independent arbitary constantsHence order of differential equation=3

Q.40. The order of the differential equation whose general solution is given by $y = (c_{1} + c_{2}) \cos (x + c_{3}) - c_{4} e^{x + C_{5}}$ where $c_{1}, c_{2}, c_{3}, c_{4}, c_{5}$ are arbitrary constants is
A) 5
B) 4
C) 3
D) 2