(Solved): Questions 4-6: If a second order linear equation is missing the y-term, then it is essentially a fi ...

Questions 4-6: If a second order linear equation is missing the $y$-term, then it is essentially a first order linear equation in terms of $y^{?}$. Therefore, it can be solved easily, even if it has non-constant coefficients by: Converting it into a first order linear equation with the substitution $u=y^{?}$, then solve the new equation for $u$ using the integrating factor method, and finally integrate the result to get $y$. Find the general solution for question 4, and find the particular solution of each initial value problem for questions 5 and 6. 4. $y^{??}+2y^{?}=4t?6e^{?2t}.$ 5. $\left(1+t^2\right)y^{??}+2t{y}^{?}=\frac{2}{1+t^2},y(0)=?2?,y^{?}(0)=u(0)=0.$ 6. $t{y}^{??}?y^{?}=t^2+t,$ $y(1)=1$, $y^{?}(1)=5$