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 y1(t)v" + [2 y'(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. t2y" - 2ty' + 2y = 4t2, t > 0, y1(t) = t y(t) = 4tet + C1t2 + c2t y(t) = 4t2lnt + c1t2 + c2t y(t) = 4tln t + C1t2 + c2t y(t) = t2et + C1t2 + c2t y(t) = 4t2lnt + c1tlnt + c2t

Explanation / Answer

Option 4rth

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