63.3.8 problem 7

Internal problem ID [13043]
Book : A First Course in Differential Equations by J. David Logan. Third Edition. Springer-Verlag, NY. 2015.
Section : Chapter 1, First order differential equations. Section 1.2 Antiderivatives. Exercises page 19
Problem number : 7
Date solved : Tuesday, January 28, 2025 at 04:50:01 AM
CAS classification : [[_2nd_order, _missing_y]]

\begin{align*} x^{\prime }+t x^{\prime \prime }&=1 \end{align*}

With initial conditions

\begin{align*} x \left (1\right )&=0\\ x^{\prime }\left (1\right )&=2 \end{align*}

✓ Solution by Maple

Time used: 0.007 (sec). Leaf size: 9

dsolve([diff(t*diff(x(t),t),t)=1,x(1) = 0, D(x)(1) = 2],x(t), singsol=all)
 

\[ x \left (t \right ) = \ln \left (t \right )+t -1 \]

✓ Solution by Mathematica

Time used: 0.018 (sec). Leaf size: 10

DSolve[{D[t*D[x[t],t],t]==1,{x[1]==0,Derivative[1][x][1 ]==2}},x[t],t,IncludeSingularSolutions -> True]
 

\[ x(t)\to t+\log (t)-1 \]