Internal problem ID [12371]
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: 6.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_linear]
\[ \boxed {y^{\prime }-\frac {2 y}{x}={\mathrm e}^{x}} \] With initial conditions \begin {align*} \left [y \left (1\right ) = {\frac {1}{2}}\right ] \end {align*}
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 29
dsolve([diff(y(x),x)=2*y(x)/x+exp(x),y(1) = 1/2],y(x), singsol=all)
\[ y \left (x \right ) = -\operatorname {Ei}_{1}\left (-x \right ) x^{2}+\operatorname {Ei}_{1}\left (-1\right ) x^{2}+\frac {x \left (2 x \,{\mathrm e}+x -2 \,{\mathrm e}^{x}\right )}{2} \]
✓ Solution by Mathematica
Time used: 0.116 (sec). Leaf size: 31
DSolve[{y'[x]==2*y[x]/x+Exp[x],{y[1]==1/2}},y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \frac {1}{2} x \left (2 x \operatorname {ExpIntegralEi}(x)-2 \operatorname {ExpIntegralEi}(1) x+2 e x+x-2 e^x\right ) \]