<jupyter_start><jupyter_text>Given that $y_1 = \frac{4}{t}$ is a solution of the differential equation $t^2 y'' + 3t y' + y = 0$, find the other solution using reduction of order.<jupyter_code>t = Symbol('t')
y, p = red_order(4 / t, *to_std(t**2, 3*t, 1), 0, t)
p.display_ipython()<jupyter_output><empty_output><jupyter_text>Given that $y_1 = e^{-\frac{b}{2a}}$ is a solution of the differential equation $a y'' + b y' + c y = 0$, find the other solution using reduction of order.<jupyter_code>a, b, c, t = symbols('a b c t', real=True)
y1 = exp(-b / (2*a) * t)
y, p = red_order(y1, *to_std(a, b, c), 0, t)
p.display_ipython()<jupyter_output><empty_output>
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