1. Solve the differential equation (4x³y² - 6x²y - 2x - 3)dx + (2x¹y-2x³)dy=02. 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 doublein 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 ofy" - 7y' +10y = 06. Find the general solution of 2y"+ 2y' + 5y = 07. Solve the initial-value problemy"-2y + y = 0, y(0) = 7, y'(0) = 4 Test B. Problem Solving. Solve the following completely1. Solve the differential equation (4x³y? – 6x²y – 2x – 3)dx + (2x'y-2x³)dy=02. The half-life of a radioactive substance is 5 days. Find the time required for a given amount ofthe 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 doublein value in 8 years?4. A thermometer reading 18°F is brought into a room where the temperature is 70°F; 1 min laterthe thermometer reading is 31°F. Find the temperature reading 5 min after the thermometer isfirst brought into the room.5. Verify using the principle of Superposition that y: = e and y2 = e* are solutions ofy" - 7y' + 10y = 06. Find the general solution of 2y"+ 2y' + 5y = 07. Solve the initial-value problemy" - 2y' + y = 0, y(0) = 7, y'(0) = 4

Since you have asked multiple question, we will solve the first question for you. If you want any…

Answered: 1. Solve the differential equation…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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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

Test B. Problem Solving. Solve the following completely
1. Solve the differential equation (4x³y? – 6x²y – 2x – 3)dx + (2x'y-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 y: = e and y2 = e* 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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