10.1.15 problem 15

Internal problem ID [1112]
Book : Elementary differential equations and boundary value problems, 10th ed., Boyce and DiPrima
Section : Section 2.1. Page 40
Problem number : 15
Date solved : Monday, January 27, 2025 at 04:33:50 AM
CAS classification : [_linear]

\begin{align*} 2 y+t y^{\prime }&=t^{2}-t +1 \end{align*}

With initial conditions

\begin{align*} y \left (1\right )&={\frac {1}{2}} \end{align*}

✓ Solution by Maple

Time used: 0.007 (sec). Leaf size: 19

dsolve([2*y(t)+t*diff(y(t),t) = t^2-t+1,y(1) = 1/2],y(t), singsol=all)
 

\[ y = \frac {t^{2}}{4}-\frac {t}{3}+\frac {1}{2}+\frac {1}{12 t^{2}} \]

✓ Solution by Mathematica

Time used: 0.029 (sec). Leaf size: 22

DSolve[{2*y[t]+t*D[y[t],t] == t^2-t+1,y[1]==1/2},y[t],t,IncludeSingularSolutions -> True]
 

\[ y(t)\to \frac {1}{12} \left (3 t^2+\frac {1}{t^2}-4 t+6\right ) \]