Differential equations questions | form six Pure Advanced Mathematics

(4114) Question Category: Mathematical Calculation

  1. Solve the differential equation frac{r an heta}{a^{2}-r^{2}}frac{d}{d heta}=1 given that r =0  when heta =frac{pi}{4}
  2. Verify that y=10sin 3x+9cos 3x is a solution of the differential equation frac{d^{2}y}{dx^{2}}+9y=0 if frac{dy}{dx}=0  when x=0.

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(4115) Question Category: Mathematical Calculation

  1. The population of a certain country doubles in 15 years. In how many years will it be six times under the assumption that the rate of increase is proportional to the number of inhabitants?.
  2. Find the particular solution of the differential equation frac{d^{2}y}{dx^{2}}+3frac{dy}{dx}+2y=cos x

Answer / Solution

UNSOLVED

(4116) Question Category: Mathematical Calculation

Form a differential equation whose general solution is y=Ae^{mx}+Be^{-mx} where A,B and m are constants.

Answer / Solution

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(5352) Question Category: Mathematical Calculation

If y=left ( frac{1-x^{2}}{1+x^{2}} ight ), show that (1-x^{4})frac{dy}{dx}+4nxy=0

Answer / Solution

UNSOLVED

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