© examsiri.com
Question : 158 of 160
Marks:
+1,
-0
Solution:
Given that
x2y−x3‌=y4‌cos‌xOn dividing by
y4, we get
‌‌−‌‌=cos‌x‌⇒‌‌‌‌=‌−cos‌x‌⇒‌‌‌‌−‌=−‌‌cos‌x‌‌ Let ‌‌‌−‌=t‌⇒‌‌‌‌=‌⋅‌‌⇒‌‌‌⋅‌+‌=‌‌cos‌x‌⇒‌‌‌+‌t=‌‌cos‌x‌ This is a linear differential equation in
t, on comparing with
‌+Pt=Q, we get
‌‌P=‌,Q=‌‌cos‌x ∴‌‌‌ I.F. ‌=e∫P‌dx=e∫‌‌dx=elog‌x3=x3∴ Complete solution is
tx3‌=3‌∫‌‌cos‌x‌dx+c1⇒tx3‌=3sin‌x+c1⇒‌‌−‌x3‌=3sin‌x+c1⇒‌‌y−3x3‌=−3sin‌x+c
© examsiri.com
Go to Question: