Question

1. Can we obtain a general solution?

2. What techniques would you use in order?

sin(t)y" + 4y = 1, Y" - sin(t)y=sin(t), Given a solution y(t) of the ODE is also provided Given two solutions y(t) and y(t) are also provided a sin(y") + b sin(y') + csin(y) = 0, a,b,c > 0 y" + 2ty' + y2 = 0, Given a solution y(t) of the ODE is provided

Answer 1

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a of onder differential squations (Is Yes, general solution Metroda @ "taty' ty=0 Converting to systems of fit is possible let y=.9 y = 9 ولا ۔ وہ Sint of first order non-line Method 1 ₂ y = yll The only way is to = sint Concert it into system 4. ya differential equation to = sint ty, sint Let S = 9 soring @ and Y, is General solation yll & y =ų © a sin (yl) + bancull t Csing zo es aty This is not possible possible by solving ① and ② direct techniques . we find "y Becaure the derivative co general solution. Annot be seperated from function - probably series solutions might work By assuming sin (yl) ay Sony)- y sin(y) ñ y for approximate solution - a as the the sine
please feel free to ask questions.Thank you.