The solution of a differential equation is y = A cos x + B sin x. If it satisfy the condition
y(0) = 2 and y(π/2) = 1 then ________.
a) A =1 and B = 2
b) A = 2 and B = 1
c) A = ½ and B = 2
d) A = 1 and B = ½
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Answers
Answered by
14
Answer:
Put x=
6
π
,we get
f(
6
π
)sin(
3
π
)−cos(
6
π
)+(1+(sin (
6
π
)
2
)f(
6
π
)=0
f(
6
π
)=
2
3
+5
2
3
Answered by
1
( 1+y1+sinx) dx
dy
=−cosx dx
dy
= (1+sinx)−(1+y)cosx
⇒ (1+y)
dy = (1+sinx)−cosx dx
Integrating both sides,
Put 1+sinx=t
⇒cosxdx=dt log∣1+y∣=∫ t−dt
⇒log∣1+y∣=−log∣1+sinx∣+logC
⇒log(1+y)(1+sinx)=logC
⇒C=(1+y)(1+sinx)
Given y(0)=1
⇒C=2
So, 2=(1+y)(1+sinx)
⇒y( 2π )=0
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