Differential Equations - Online Test
Q1. Find the particular solution of the differential equation , given that y = 0 and x = 0.
Answer : Option D
Explaination / Solution:
Q2. In a bank, principal increases continuously at the rate of r% per year. Find the value of r if Rs 100 double itself in 10 years (loge2 = 0.6931).
Answer : Option B
Explaination / Solution:
Let P be the principal at any time t. then,
When P = 100 and t = 0., then, c = 100, therefore, we have:
Now, let t = T, when P = 100., then;
When P = 100 and t = 0., then, c = 100, therefore, we have:
Now, let t = T, when P = 100., then;
Q3. In a bank, principal increases continuously at the rate of 5% per year. An amount of Rs1000 is deposited with this bank, how much will it worth after 10 years
Answer : Option D
Explaination / Solution:
Here P is the principal at time t
When P = 1000 and t = 0 ., then ,
c = 1000, therefore, we have :
When P = 1000 and t = 0 ., then ,
c = 1000, therefore, we have :
Q4. Solution of is
Answer : Option C
Explaination / Solution:
Q5. General solution of is
Answer : Option B
Explaination / Solution:
Q6. To form a differential equation from a given function
Answer : Option A
Explaination / Solution:
We shall differentiate the function equal to the number of arbitrary constant so that we get equations equal to arbitrary constant and then eliminate them to form a differential equation
Q7. Forming a differential equation representing the given family of curves by eliminating arbitrary constants a and b fromyields the differential equation
Answer : Option B
Explaination / Solution:
Q8.
Forming a differential equation representing the given family of curves by eliminating arbitrary constants a and b from yields the differential equation
Answer : Option A
Explaination / Solution:
2yy′=−2xyy′=−xyy′′+y′2+1=0
Q9. Forming a differential equation representing the given family of curves by eliminating arbitrary constants a and b from yields the differential equation
Answer : Option A
Explaination / Solution:
Q10.
Forming a differential equation representing the given family of curves by eliminating arbitrary constants a and b from yields the differential equation
Answer : Option C
Explaination / Solution:
