Internal problem ID [12333]
Book: Ordinary Differential Equations by Charles E. Roberts, Jr. CRC Press. 2010
Section: Chapter 2. The Initial Value Problem. Exercises 2.2, page 53
Problem number: 17.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_linear]
\[ \boxed {y^{\prime }-y x=\frac {1}{x^{2}+1}} \] With initial conditions \begin {align*} [y \left (-5\right ) = 0] \end {align*}
✓ Solution by Maple
Time used: 0.032 (sec). Leaf size: 31
dsolve([diff(y(x),x)=x*y(x)+1/(1+x^2),y(-5) = 0],y(x), singsol=all)
\[ y \left (x \right ) = \left (\int _{-5}^{x}\frac {{\mathrm e}^{-\frac {\textit {\_z1}^{2}}{2}}}{\textit {\_z1}^{2}+1}d \textit {\_z1} \right ) {\mathrm e}^{\frac {x^{2}}{2}} \]
✓ Solution by Mathematica
Time used: 0.478 (sec). Leaf size: 41
DSolve[{y'[x]==x*y[x]+1/(1+x^2),{y[-5]==0}},y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to e^{\frac {x^2}{2}} \int _{-5}^x\frac {e^{-\frac {1}{2} K[1]^2}}{K[1]^2+1}dK[1] \]