Question
The solution of y2−7y1+12y=0 is
Answer: Option A
:
A
The given equation can be written as (ddx−3)(dydx−4y)=0....(i)
If dydx−4y=u then (I) reduces to dudx−3u=0
⇒duu=3dx⇒u=C1e3x.Therefore, we have dydx−4y=C1e3xwhich is a linear equation whose I.F.is e−4x. So ddx(ye−4x)=C1e−x
⇒ye−4x=−C1e−x+C2⇒y=C1e3x+C2e4x
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:
A
The given equation can be written as (ddx−3)(dydx−4y)=0....(i)
If dydx−4y=u then (I) reduces to dudx−3u=0
⇒duu=3dx⇒u=C1e3x.Therefore, we have dydx−4y=C1e3xwhich is a linear equation whose I.F.is e−4x. So ddx(ye−4x)=C1e−x
⇒ye−4x=−C1e−x+C2⇒y=C1e3x+C2e4x
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