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State whether the following statements are true or false. Justify your answers with thehelp of a short proof or a counter-example. (10) i) ny′ + P(x) y = Q(x) y is a linear equation for integral values of n. ii) ,0 y = is a singular solution of the differential equation 27 8 .03 =−dxdyy iii) 2 41xy + yis an integrating factor for the differential equation ( ) ( ) .02 2 3 3x y + y dx + y − x dy = iv) Equation 2 2x ( y − px) = yp is reducible to clairaut’s form. v) x2 is a particular integral for . e 2xy′ − y = e |
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