4. The Euler-Cauchy Equation is a linear, second-order variable coefficient differential equation of the form

at2y" + bty' + cy=0, t > 0

where a, b, c R and a 0. Using the substitution y = t" and proceeding as we did for the constant coefficient case, you

can find a characteristic equation for the differential equation. Distinct solutions r₁ and r2 of this characteristic equation can

be used to find a basis for the solution space of the differential equation. Employ this technique to find the general solution of

4t²y" +8ty' - 3y = 0, t > 0.