Answer:
Verified
Step-by-step explanation:
Question:-
- We are given the following non-homogeneous ODE as follows:
- A general solution to the above ODE is also given as:
- We are to prove that every member of the family of curves defined by the above given function ( y ) is indeed a solution to the given ODE.
Solution:-
- To determine the validity of the solution we will first compute the first derivative of the given function ( y ) as follows. Apply the quotient rule.
- Now we will plug in the evaluated first derivative ( y' ) and function ( y ) into the given ODE and prove that right hand side is equal to the left hand side of the equality as follows:
- The equality holds true for all values of " C "; hence, the function ( y ) is the general solution to the given ODE.
- To determine the complete solution subjected to the initial conditions y (1) = 3. We would need the evaluate the value of constant ( C ) such that the solution ( y ) is satisfied as follows:
- Therefore, the complete solution to the given ODE can be expressed as:
- To determine the complete solution subjected to the initial conditions y (3) = 1. We would need the evaluate the value of constant ( C ) such that the solution ( y ) is satisfied as follows:
- Therefore, the complete solution to the given ODE can be expressed as:
Answer:
81
Step-by-step explanation:
6 over 12 equals 3 over 6 6 over 3 equals 6 over 12 6 over 6 equals 3 over 12 12 over 6 equals 3 over 6
Answer:
6/1000
Step-by-step explanation:
.0006 times 10,000
A=x
B= 2x
C=3x
If you add them up =
6x =180
÷6 both sides
x=30
A=30
B=60
C=90
one angle is 90 degrees so the triangle is classified as a right triangle
Answer:
Step-by-step explanation:
35/4 = 8.75 or 8 3/4