Find the particular solution of the differential equation x^2/(y^2-4)dy/dx=1/2y

Question

Find the particular solution of the differential equation
x^2/(y^2-4)dy/dx=1/2y
satisfying the initial condition y(1)=sqrt{5}.

Answer: y=

Your answer should be a function of x.

Explanation / Answer

x^2 / (y^2-4) dy/dx = 1 / 2y => 2y / (y^2 - 4) dy = dx / x^2 => ?d(y^2 - 4) / (y^2 - 4) = ?dx / x^2 = ln l y^2 - 4 l = - 1/x + c Plugging x = 1 => y = v5 Integration = ln l 5 - 4 l = - 1 + c => c = 1 => ln l y^2 - 4 l = - 1/x + 1 => y^2 - 4 = e^(1 - 1/x) [On further simplification, you get y2 = 4 + e^(1 - 1/x) = lne^4 + lne^(1 - 1/x) => y^2 = ln e^[4(1 - 1/x)] => y = ±v[ ln e^[4(1 - 1/x)] ]

Related Questions

Navigate

• Browse (All)
• Browse F
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.