Internal problem ID [519]
Book: Elementary differential equations and boundary value problems, 10th ed., Boyce and
DiPrima
Section: Section 2.4. Page 76
Problem number: 4.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_linear]
Solve \begin {gather*} \boxed {2 y t +\left (-t^{2}+4\right ) y^{\prime }-3 t^{2}=0} \end {gather*} With initial conditions \begin {align*} [y \left (-3\right ) = 1] \end {align*}
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 42
dsolve([2*t*y(t)+(-t^2+4)*diff(y(t),t) = 3*t^2,y(-3) = 1],y(t), singsol=all)
\[ y \relax (t ) = \frac {3 t}{2}-\frac {3 \ln \left (t -2\right ) t^{2}}{8}+\frac {3 \ln \left (t -2\right )}{2}+\frac {3 \ln \left (2+t \right ) t^{2}}{8}-\frac {3 \ln \left (2+t \right )}{2}+\frac {11 t^{2}}{10}-\frac {22}{5}+\frac {3 \ln \relax (5) t^{2}}{8}-\frac {3 \ln \relax (5)}{2} \]
✓ Solution by Mathematica
Time used: 0.054 (sec). Leaf size: 55
DSolve[{2*t*y[t]+(-t^2+4)*y'[t] == 3*t^2,y[-3]==1},y[t],t,IncludeSingularSolutions -> True]
\begin{align*} y(t)\to \frac {1}{40} \left (44 t^2-15 i \pi \left (t^2-4\right )-15 \left (t^2-4\right ) \log (2-t)+15 \left (t^2-4\right ) \log (5 (t+2))+60 t-176\right ) \\ \end{align*}