79.1.24 problem 4 (vi)

Internal problem ID [18511]
Book : Elementary Differential Equations. By R.L.E. Schwarzenberger. Chapman and Hall. London. First Edition (1969)
Section : Chapter 3. Solutions of first-order equations. Exercises at page 47
Problem number : 4 (vi)
Date solved : Tuesday, January 28, 2025 at 11:51:33 AM
CAS classification : [_linear]

\begin{align*} x^{\prime } t +x \ln \left (t \right )&=t^{2} \end{align*}

✓ Solution by Maple

Time used: 0.000 (sec). Leaf size: 25

dsolve(t*diff(x(t),t)+x(t)*ln(t)=t^2,x(t), singsol=all)
 

\[ x = \left (\int t \,{\mathrm e}^{\frac {\ln \left (t \right )^{2}}{2}}d t +c_{1} \right ) {\mathrm e}^{-\frac {\ln \left (t \right )^{2}}{2}} \]

✓ Solution by Mathematica

Time used: 0.088 (sec). Leaf size: 48

DSolve[t*D[x[t],t]+x[t]*Log[t]==t^2,x[t],t,IncludeSingularSolutions -> True]
 

\[ x(t)\to \frac {1}{2} e^{-\frac {1}{2} \log ^2(t)-2} \left (\sqrt {2 \pi } \text {erfi}\left (\frac {\log (t)+2}{\sqrt {2}}\right )+2 e^2 c_1\right ) \]