Differential Equations

Q1.The solution of dy/dx = y/x + tan(y/x) is:

• Asin(y/x) = Cx
• Bx sin(y/x) = C
• Csin(y/x) = C/x
• Dcos(y/x) = Cx

Q2.The integrating factor (IF) of the linear DE dy/dx + P(x)y = Q(x) is:

• Ae^∫P dx
• Be^P
• C∫P dx
• De^∫Q dx

Q3.The solution of (1+x²) dy/dx + 2xy = cos x is found using IF =

• A1 + x²
• Be^(arctan x)
• Cx²
• D1/(1+x²)

Q4.Verify that y = (ax + b)/(a² + b²) is not a solution (find the correct substitution approach): The solution of y' = (y+1)/(x+1) with y(0) = 2 is:

• Ay = 3(x+1) – 1
• By = 2x + 1
• Cy = 3x + 2
• Dy + 1 = 3(x + 1)

Q5.The solution of dy/dx = (x + y)/(x – y) (a homogeneous DE) after substitution y = vx gives:

• Av + x dv/dx = (1+v)/(1–v)
• Bx dv/dx = (1+v)/(1–v) – v
• CBoth (a) and (b) together describe the process
• DOnly option (b) is the correct transformed equation