1. Solve the differential equation (4x*y² - 6x°y – 2x – 3)dx + (2x*y-2x³)dy=0
1. Solve the differential equation (4x³y² - 6x²y - 2x - 3)dx + (2x¹y-2x³)dy=0
2. The half-life of a radioactive substance is 5 days. Find the time required for a given amount of the material to decay to 30% of its original mass. 3. At what rate of interest, compounded continuously, will a bank deposit of 15, 000 pesos double
in value in 8 years? 4. A thermometer reading 18°F is brought into a room where the temperature is 70°F; 1 min later the thermometer reading is 31°F. Find the temperature reading 5 min after the thermometer is first brought into the room.
5. Verify using the principle of Superposition that y₁ = e² and y2 = ex are solutions of
y" - 7y' +10y = 0
6. Find the general solution of 2y"+ 2y' + 5y = 0
7. Solve the initial-value problem
y"-2y + y = 0, y(0) = 7, y'(0) = 4
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