# Differential Equations – Exercise – 1

1. The solution of a differential equation which is not obtained from the general solution is known as :

(a) Particular solution
(b) Singular solution
(c) Complete solution
(d ) Auxiliary solution

Explanation
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2. The differential equation dy/dx = y2 is :

(a) Linear
(b) Non-linear
(c) Quasilinear
(d ) None of these

Explanation
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3. The differential equation formed by y= acos+ bsin+ 4 where a and b are arbitrary constants is :

(a) (d2y/dx2) + y = 0
(b) (d2y/dx2) – y = 0
(c) (d2y/dx2) + y = 4
(d) (d2y/dx2) – y = 4

Explanation
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4. The general solution of (x2 D2 – xD), y= 0 is :

(a) y = C1 + C2 ex
(b) y = C1 + Cx
(c) y = C1 + C2 x2
(d) y = C1 x + C2 x2

Explanation
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5. The equation a0 x2y″+ a1xy′+ a2y = φ(x) is called :

(a) Legendre’s linear equation
(b) Cauchy’s linear equation
(c) Simultaneous equation
(d) Method of undetermined coefficients