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:
28980
Step-by-step explanation:
Also "<em>nice</em>"
I think the slope would be 1.5
explanation: i’m not sure but rise/run,
y2-y1/x2-x1
(1,1.5) (4,6)
6-1.5/4-1=4.5/3=1.5
Answer:
<em>B) -7x + 7y = -49</em>
Step-by-step explanation:
This is a y=x plot/line shifted by 7 units.
This can also be verified plugging in the values of x=0,y=-7 and x=7,y=0. The only equation which satisfies these points in Equation B. These points have been chosen as they're the intercepts of this plot.
Answer:
Yes
Step-by-step explanation:
Since the triangles have two congruent angles, the third angle is also congruent.
The sides of one triangle are proportional to the corresponding sides of the other triangle.