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To reduce the differential equation (dy / dx) + P (x) . y = Q (x) . yⁿ to the linear form, the substitution is

1) v = 1 / yn 2) v = 1 / yn-1 3) v = yn 4) v = yn-1... View Article

1) 2x = sin y (1 + cx2) 2) (y / sin x) + log x = c 3) log... View Article

1) y = (x + 2) + cex 2) y = – (x + 2) + cex 3) x =... View Article

1) y sin x = c + sin 2x 2) y cos x = c + (1 / 2) sin... View Article

1) x 2) x2/2 3) 1/x 4) 1/x2 5) 1/2x Solution: (3) 1/x \(\begin{array}{l}\begin{array}{l} \text { Given that, } I... View Article

1) y (1 – x2) = tan-1 x + c 2) y (1 + x2) = tan-1 x + c... View Article

1) 3x (1 + y2) = 4y3 + c 2) 3y (1 + x2) = 4x3 + c 3) 3x... View Article

1) y = ex cos x + c 2) y cos x = ex + c 3) y = ex... View Article

1) y = x log x + x 2) y = log x + x 3) y = x log... View Article

1) ex 2) log x 3) log (logx) 4) x Solution: (2) log x \(\begin{array}{l}x \log x \frac{d y}{d x}+y=2... View Article

1) 1/log y 2) log (log y) 3) 1 + log y 4) 1/log (log y) 5) log y Solution:... View Article

1) y = 2(ex + x – 1) 2) y = 2(ex – x – 1) 3) y = 2(ex... View Article

1) x 2) 2x 3) ex log x 4) x ex Solution: (4) x ex \(\begin{array}{l}x \frac{d y}{d x}+(1+x) y=x\\... View Article

1) sec x = (tan x + C) y 2) y sec x = tan x + C 3) y... View Article

1) y – log x – 1 = Cx 2) x + log y + 1 = Cx 3) y... View Article

1) x = y3 + Cy 2) x = y2 + Cy 3) x3 = y3 + Cy 4) None... View Article

1) – (1/2) 2) e + 1/2 3) e – 1/2 4) 1/2 Solution: (1) – (1/2) \(\begin{array}{l}\frac{d y}{d t}-\left(\frac{t}{1+t}\right)... View Article

1) y = (x4 / 5) + (c / x) 2) y = (x3 / 3) + (c / x)... View Article

1) xsec y = tan y + C 2) tan y – sec y = Cx 3) tan y +... View Article

1) y x sec y = C + tan x 2) yx cos y = C + tan x 3)... View Article