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]
\[ \boxed {2 y t +\left (-t^{2}+4\right ) y^{\prime }=3 t^{2}} \] With initial conditions \begin {align*} [y \left (1\right ) = -3] \end {align*}
✓ Solution by Maple
Time used: 0.063 (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)
\[ y \left (t \right ) = -6+\frac {3 \left (t^{2}-4\right ) \ln \left (2+t \right )}{8}+\frac {3 i \pi \,t^{2}}{8}-\frac {3 \ln \left (3\right ) t^{2}}{8}-\frac {3 \ln \left (t -2\right ) t^{2}}{8}-\frac {3 i \pi }{2}+\frac {3 t^{2}}{2}+\frac {3 t}{2}+\frac {3 \ln \left (3\right )}{2}+\frac {3 \ln \left (t -2\right )}{2} \]
✓ Solution by Mathematica
Time used: 0.043 (sec). Leaf size: 52
DSolve[{2*t*y[t]+(-t^2+4)*y'[t] == 3*t^2,y[1]==-3},y[t],t,IncludeSingularSolutions -> True]
\[ y(t)\to -\frac {3}{8} \left (-4 t^2+t^2 \log (3)+\left (t^2-4\right ) \log (2-t)-\left (t^2-4\right ) \log (t+2)-4 t+16-4 \log (3)\right ) \]