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Class 12

Homogeneous and Linear Equations, with Mixed Practice — Quiz

Five questions on homogeneous and linear differential equations. Pick one answer for each.

5 questions, one mark each. 3 to pass. Suggested time: 10 minutes. Your answers are not recorded.

  1. The integrating factor of dydx+3y=x\displaystyle \dfrac{dy}{dx} + 3y = x is
  2. The integrating factor of dydx+yx=x2\displaystyle \dfrac{dy}{dx} + \dfrac{y}{x} = x^2 (for x>0x > 0) is
  3. The general solution of dydx−y=e3x\displaystyle \dfrac{dy}{dx} - y = e^{3x} is
  4. To solve the homogeneous equation dydx=x2+y23xy\displaystyle \dfrac{dy}{dx} = \dfrac{x^2 + y^2}{3xy}, the standard substitution is
  5. Solve dydx=x+2yx\displaystyle \dfrac{dy}{dx} = \dfrac{x + 2y}{x}.
Unanswered questions are marked wrong.

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