10.3.4 problem 4

Internal problem ID [1169]
Book : Elementary differential equations and boundary value problems, 10th ed., Boyce and DiPrima
Section : Section 2.4. Page 76
Problem number : 4
Date solved : Monday, January 27, 2025 at 04:39:08 AM
CAS classification : [_linear]

\begin{align*} 2 y t +\left (-t^{2}+4\right ) y^{\prime }&=3 t^{2} \end{align*}

With initial conditions

\begin{align*} y \left (-3\right )&=1 \end{align*}

✓ Solution by Maple

Time used: 0.029 (sec). Leaf size: 55

dsolve([2*t*y(t)+(-t^2+4)*diff(y(t),t) = 3*t^2,y(-3) = 1],y(t), singsol=all)
 

\[ y = \frac {3 t}{2}-\frac {3 \ln \left (t -2\right ) t^{2}}{8}+\frac {3 \ln \left (t -2\right )}{2}+\frac {3 \ln \left (2+t \right ) t^{2}}{8}-\frac {3 \ln \left (2+t \right )}{2}+\frac {11 t^{2}}{10}-\frac {22}{5}+\frac {3 \ln \left (5\right ) t^{2}}{8}-\frac {3 \ln \left (5\right )}{2} \]

✓ Solution by Mathematica

Time used: 0.050 (sec). Leaf size: 67

DSolve[{2*t*y[t]+(-t^2+4)*D[y[t],t] == 3*t^2,y[-3]==1},y[t],t,IncludeSingularSolutions -> True]
 

\[ y(t)\to \frac {1}{40} \left (-15 i \pi t^2+44 t^2+15 t^2 \log (5)-15 \left (t^2-4\right ) \log (2-t)+15 \left (t^2-4\right ) \log (t+2)+60 t+60 i \pi -176-60 \log (5)\right ) \]