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]
\[ \boxed {2 y t +\left (-t^{2}+4\right ) y^{\prime }=3 t^{2}} \] With initial conditions \begin {align*} [y \left (-3\right ) = 1] \end {align*}
✓ Solution by Maple
Time used: 0.031 (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)
\[ y \left (t \right ) = \frac {3 t}{2}+\frac {3 \ln \left (2+t \right ) t^{2}}{8}-\frac {3 \ln \left (2+t \right )}{2}-\frac {3 \ln \left (t -2\right ) t^{2}}{8}+\frac {3 \ln \left (t -2\right )}{2}+\frac {11 t^{2}}{10}-\frac {22}{5}+\frac {3 \ln \left (5\right ) t^{2}}{8}-\frac {3 \ln \left (5\right )}{2} \]
✓ Solution by Mathematica
Time used: 0.049 (sec). Leaf size: 67
DSolve[{2*t*y[t]+(-t^2+4)*y'[t] == 3*t^2,y[-3]==1},y[t],t,IncludeSingularSolutions -> True]
\[ y(t)\to \frac {1}{40} \left (-15 i \pi t^2+44 t^2+15 t^2 \log (5)-15 \left (t^2-4\right ) \log (2-t)+15 \left (t^2-4\right ) \log (t+2)+60 t+60 i \pi -176-60 \log (5)\right ) \]