Question

2. Solve the following Bernoullis differential equations. (a) 2204 + 2xy – 2,2 = 0 (b) = 54 – 3y2 (c) y 2 x +48 = 1 (d) copy
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* answer :- (a) given differntial ef is x2 dy +24a - 43=0 da ie uzdy tray= 43 - do which is Bernoullis differential eq x²dy +Spradda fa da Ize =e = e 45 de - 4loge ze I = eloga - 7 = 4 > I- solution is u.I= (arn). I da to Cc is constant integration)(b) dy = 54 - 342 dy +34²=54 da dy - 5y=-34² da Dividing both side by y I dy - 54 =-3. 42 dx 42 :. 4²y-syl = -3 put y=u Dify e 3 + c 5 y = 3 otce sa IC dividing by both side by esa) which is required solution co) y ² dy + y = 1 42 dy do 1 -4 2 0 da

solution of L.DE is u. I=SQ12). I da to :. u. eBa_13. e3x dx + c 4 e 3 = 35e3x dx tc :. 43. 3x _ Xe to 43. 3 4 _ 3 to 1. y3 =Eq become. -3 du + e u=3 du - uz which is einear elifferential ear 10gx2 C = e Here pox) = -2 & Q60 = -1 I= S-2 do -25 62 -2By using the definition of Bernoullis equation and using rules for solving Bernoullis equation.

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2. Solve the following Bernoulli's differential equations. (a) 2204 + 2xy – 2,2 = 0 (b)...
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