71.7.4 problem 4

Internal problem ID [14425]
Book : Ordinary Differential Equations by Charles E. Roberts, Jr. CRC Press. 2010
Section : Chapter 2. The Initial Value Problem. Exercises 2.3.3, page 71
Problem number : 4
Date solved : Tuesday, January 28, 2025 at 06:30:37 AM
CAS classification : [_linear]

\begin{align*} y^{\prime }&=\frac {y}{x -1}+x^{2} \end{align*}

With initial conditions

\begin{align*} y \left (0\right )&=1 \end{align*}

✓ Solution by Maple

Time used: 0.022 (sec). Leaf size: 23

dsolve([diff(y(x),x)=y(x)/(x-1)+x^2,y(0) = 1],y(x), singsol=all)
 

\[ y = \left (\frac {x^{2}}{2}+x +\ln \left (x -1\right )-1-i \pi \right ) \left (x -1\right ) \]

✓ Solution by Mathematica

Time used: 0.060 (sec). Leaf size: 29

DSolve[{D[y[x],x]==y[x]/(x-1)+x^2,{y[0]==1}},y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to (x-1) \left (\int _0^x\frac {K[1]^2}{K[1]-1}dK[1]-1\right ) \]