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7:00 AM JD! all call GD, , € _ Differential Equations..., , (vi), The given equation reduces to (D)y = Z, a function of z., Solve it and replace z by log x., 14. RULE TO SOLVE THE EQUATION, , , , , , , , a m-1 n-2, a,(a + bx) -t +ay(a+bx)™? ot +a;(a+bx)™* at fis, + a,..(a+ be +a,yy=X, , where ay 81, ay) ..., 4, are constants and X is a function of x., Put a + bx = e* so that z = log (a + bx) and, , De © then (a + bx) © =bD,, a, (a + bx? Oa = b*D(D-1), a, (a+ bx)? oy = HIXD - 1XD - 2), , The given equation reduces to f(D)y = Z, a function of z., Solve it and replace z by log (a + bx)., , < | >