(vi) y =e2 (a+bx)
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y = e2x (a + bx) …(1)
differentiating w.r.t x, we get
⇒ y1= e2x (0 + b) + (a + bx) e2x 2
⇒ y1 = e2xxb + (a + bx) e2x 2 ….(2)
putting (1) in (2),
y1 = be2x + 2y
⇒ y1 – 2y = b e2x ….(3)
again differentiating w.r.t x,
we get y2 – 2y1 = b.e2x.2 ….(4)
putting (3) in (4) we get
y2 – 2y1 = 2y1 – 4y
⇒ y2 – 4y1 + 4y = 0
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