71.4.17 problem 17

Internal problem ID [14389]
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
Date solved : Tuesday, January 28, 2025 at 06:29:20 AM
CAS classification : [_linear]

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

With initial conditions

\begin{align*} y \left (-5\right )&=0 \end{align*}

Solution by Maple

Time used: 0.523 (sec). Leaf size: 31

dsolve([diff(y(x),x)=x*y(x)+1/(1+x^2),y(-5) = 0],y(x), singsol=all)
 
\[ y = \left (\int _{-5}^{x}\frac {{\mathrm e}^{-\frac {\textit {\_z1}^{2}}{2}}}{\textit {\_z1}^{2}+1}d \textit {\_z1} \right ) {\mathrm e}^{\frac {x^{2}}{2}} \]

Solution by Mathematica

Time used: 0.191 (sec). Leaf size: 41

DSolve[{D[y[x],x]==x*y[x]+1/(1+x^2),{y[-5]==0}},y[x],x,IncludeSingularSolutions -> True]
 
\[ y(x)\to e^{\frac {x^2}{2}} \int _{-5}^x\frac {e^{-\frac {1}{2} K[1]^2}}{K[1]^2+1}dK[1] \]