Answer: y = eˣ/2 + Ce-x.
- A y = (x+C)e-x
- B y = eˣ/2 + Ce-x
- C y = eˣ + C
- D y = Cex
Correct answer: B. y = eˣ/2 + Ce-x
Explanation: IF = eintegral 1 dx = eˣ. Multiply: (yeˣ)' = e²ˣ. yeˣ = e²ˣ/2 + C. y = eˣ/2 + Ce-x.
The general solution y=Ax² represents an entire FAMILY of curves, one for each value of the arbitrary constant A; a particular solution (fixed by an initial condition) selects exactly one curve from this family.
Concept context
Equations involving derivatives and their solutions