What is the solution for y^'+1/2*y= 3/2*t ?

The solution for y^'+1/2*y= 3/2*t is y=3(t-2)+(c_{1})/(e^{t/2)}

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y^'+1/2y= 3/2t

y^{^{'}} + \frac{1}{2} \cdot y = \frac{3}{2} \cdot t

y = 3 (t - 2) + \frac{c _{1}}{e ^{\frac{t}{2}}}

Solution steps

y^{'} (t) + \frac{1}{2} \cdot y = \frac{3}{2} \cdot t

Solve linear ODE:

y = 3 (t - 2) + \frac{c _{1}}{e ^{\frac{t}{2}}}

y = 3 (t - 2) + \frac{c _{1}}{e ^{\frac{t}{2}}}

What is the solution for y^'+1/2*y= 3/2*t ?
The solution for y^'+1/2*y= 3/2*t is y=3(t-2)+(c_{1})/(e^{t/2)}