The method of reduction of order can also be used for the non-homogenous equatio

Question

The method of reduction of order can also be used for the non-homogenous equation y" + p(t) y' + q(t)y= g(t) provided one solution y1 of the corresponding homogenous equation is known. Let y = v( t) y1(t). y satisfies the equation above if v is a solution of y 1(t)v" + [2y'1(t) + p(t)y1(t) ]v' = g(t) This equation is a first order linear equation for v'. Solving this equation, integrating the result, and then multiplying by y1(t) leads to the general solution of the first equation. Use the method above to solve the given differential equation. ty" - (1 + t)y' + y= 17t2e2t, t > 0, y1(t) = 1 + r y(t) = 17/2 te t + c1 et + c2(t + 1) y(t) = 1/2(t+1)e t+c1et + c2(t-1) y(t) = 1/2(t-1)e2t+c1et+c2(t+1) y(t) = 17(t + 1)2 e 2t + C1et + c2(t - 1) y(t) = 17/2 (t - 1)e 2t + c1et+ c2(t+1)

Explanation / Answer

E

Related Questions

Navigate

• Browse (All)
• Browse T
• Subjects

---

---

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