10.3.5 problem 5

Internal problem ID [1170]
Book : Elementary differential equations and boundary value problems, 10th ed., Boyce and DiPrima
Section : Section 2.4. Page 76
Problem number : 5
Date solved : Monday, January 27, 2025 at 04:39:10 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 (1\right )&=-3 \end{align*}

✓ Solution by Maple

Time used: 0.046 (sec). Leaf size: 60

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

\[ y = -6+\frac {3 \left (t^{2}-4\right ) \ln \left (2+t \right )}{8}+\frac {3 i \pi \,t^{2}}{8}-\frac {3 \ln \left (3\right ) t^{2}}{8}-\frac {3 \ln \left (t -2\right ) t^{2}}{8}-\frac {3 i \pi }{2}+\frac {3 t^{2}}{2}+\frac {3 t}{2}+\frac {3 \ln \left (3\right )}{2}+\frac {3 \ln \left (t -2\right )}{2} \]

✓ Solution by Mathematica

Time used: 0.042 (sec). Leaf size: 52

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

\[ y(t)\to -\frac {3}{8} \left (-4 t^2+t^2 \log (3)+\left (t^2-4\right ) \log (2-t)-\left (t^2-4\right ) \log (t+2)-4 t+16-4 \log (3)\right ) \]