4.3.4 problem 4

Internal problem ID [1169]
Book : Elementary differential equations and boundary value problems, 10th ed., Boyce and DiPrima
Section : Section 2.4. Page 76
Problem number : 4
Date solved : Tuesday, September 30, 2025 at 04:27:10 AM
CAS classification : [_linear]

\begin{align*} 2 t y+\left (-t^{2}+4\right ) y^{\prime }&=3 t^{2} \end{align*}

With initial conditions

\begin{align*} y \left (-3\right )&=1 \\ \end{align*}

✓ Maple. Time used: 0.051 (sec). Leaf size: 55

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

\[ y = \frac {3 t}{2}+\frac {3 \ln \left (t +2\right ) t^{2}}{8}-\frac {3 \ln \left (t +2\right )}{2}-\frac {3 \ln \left (t -2\right ) t^{2}}{8}+\frac {3 \ln \left (t -2\right )}{2}+\frac {11 t^{2}}{10}-\frac {22}{5}+\frac {3 \ln \left (5\right ) t^{2}}{8}-\frac {3 \ln \left (5\right )}{2} \]

✓ Mathematica. Time used: 0.031 (sec). Leaf size: 67

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

\begin{align*} 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 ) \end{align*}

✓ Sympy. Time used: 0.277 (sec). Leaf size: 71

from sympy import * 
t = symbols("t") 
y = Function("y") 
ode = Eq(-3*t**2 + 2*t*y(t) + (4 - t**2)*Derivative(y(t), t),0) 
ics = {y(-3): 1} 
dsolve(ode,func=y(t),ics=ics)
 

\[ y{\left (t \right )} = - \frac {3 t^{2} \log {\left (t - 2 \right )}}{8} + \frac {3 t^{2} \log {\left (t + 2 \right )}}{8} + t^{2} \left (\frac {3 \log {\left (5 \right )}}{8} + \frac {11}{10}\right ) + \frac {3 t}{2} + \frac {3 \log {\left (t - 2 \right )}}{2} - \frac {3 \log {\left (t + 2 \right )}}{2} - \frac {22}{5} - \frac {3 \log {\left (5 \right )}}{2} \]