Internal problem ID [12369]
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.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_linear]
\[ \boxed {y^{\prime }-\frac {y}{x -1}=x^{2}} \] With initial conditions \begin {align*} [y \left (0\right ) = 1] \end {align*}
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 24
dsolve([diff(y(x),x)=y(x)/(x-1)+x^2,y(0) = 1],y(x), singsol=all)
\[ y \left (x \right ) = -\left (x -1\right ) \left (i \pi -\frac {x^{2}}{2}-x -\ln \left (x -1\right )+1\right ) \]
✓ Solution by Mathematica
Time used: 0.06 (sec). Leaf size: 31
DSolve[{y'[x]==y[x]/(x-1)+x^2,{y[0]==1}},y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \frac {1}{2} (x-1) \left (x^2+2 x+2 \log (x-1)-2 i \pi -2\right ) \]