Internal problem ID [520]
Book: Elementary differential equations and boundary value problems, 10th ed., Boyce and
DiPrima
Section: Section 2.4. Page 76
Problem number: 5.
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 \relax (1) = -3] \end {align*}
✓ Solution by Maple
Time used: 0.031 (sec). Leaf size: 46
dsolve([2*t*y(t)+(-t^2+4)*diff(y(t),t) = 3*t^2,y(1) = -3],y(t), singsol=all)
\[ y \relax (t ) = \frac {\left (3 i \pi -3 \ln \relax (3)+3 \ln \left (2+t \right )-3 \ln \left (t -2\right )+12\right ) t^{2}}{8}+\frac {3 t}{2}-\frac {3 i \pi }{2}+\frac {3 \ln \relax (3)}{2}-\frac {3 \ln \left (2+t \right )}{2}+\frac {3 \ln \left (t -2\right )}{2}-6 \]
✓ Solution by Mathematica
Time used: 0.047 (sec). Leaf size: 41
DSolve[{2*t*y[t]+(-t^2+4)*y'[t] == 3*t^2,y[1]==-3},y[t],t,IncludeSingularSolutions -> True]
\begin{align*} y(t)\to \frac {3}{8} \left (4 \left (t^2+t-4\right )-\left (t^2-4\right ) \log (6-3 t)+\left (t^2-4\right ) \log (t+2)\right ) \\ \end{align*}