Answer: y = eˣ/2 + Ce -x.
- A y = (x+C)e<sup>-x</sup>
- B y = eˣ/2 + Ce<sup>-x</sup>
- C y = eˣ + C
- D y = Ce<sup>x</sup>
Correct answer: B. y = eˣ/2 + Ce<sup>-x</sup>
Explanation: IF = e<sup>integral 1 dx</sup> = eˣ. Multiply: (yeˣ)' = e²ˣ. yeˣ = e²ˣ/2 + C. y = eˣ/2 + Ce<sup>-x</sup>.
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