a) f(x), g(x) and h(x) are c) W (f(x), g(x), h(x)) = 0 d) W (f 02) 6-1 (22) H a)-2coshnt b)-2sinhnt c)-2cosnt d)-2sinnt Q3) The Integrating factor which make (3x²y + 2xy + y³)dx + (x² + y²)dy = 0 exact, is: a) e-3x b) ex c) ex d) ex Q4) The linear form of nonlinear ODE y' - 2y = 2y, is: a) u' + 6u = -6 b) u'-6u = -6 c) u' - 6u = 6 d) u' + 6u = 6 Q5) The general solution of 2x2y" + 3xy' - 15y = 0, is: a) y(x) = c₂x² + ₂x³ b) y(x) = ₂x + ₂x-3 S ©)x(x) = GX+G d) y(x) = ₂x + ₂x³ -0.5 cos3t): Q6) Evaluate L (2e-2t sin4t 8 8 a) b) (-2)³+16 S 2s² +18 (s+2)+16 c)(8+2)³+16 25³ +18 25² +18 (s-2)³ +16 b)y(t) = cet cos(√5 t) + c₂e²sin (√5t) d) y(t) = Gel cos(5 t) + c₂e²sin (5 t) Q7) The general solution of y"-4y' +9y = 0, is: a) y(t) = c₁e²t cos(5 t) + c₂e²t sin (5 t) c)y(t) = c₂e²t cos(√5 t) + c₂e2tsin (√5 t) Q8) The inverse Laplace transform of H(s) +²e² c) f(t) ==e+e-2t is: * (3+2)(x-2) -2t a) f(t) == b) f(t) ==e+ d)f(t) == +²t Q9) The solution of y"+y' = 0 by using power series method, is: *** a) y(x) = a + a₁ (1- .) 31 41 St 24 c) y(x) = a + a₁(x-+ 41 51 2s²+18 2/52/5 + b) y(x) = a + a₂(1+-+- d)y(x) = a + a₂(x + - + +)