Internal problem ID [12358]
Book: Ordinary Differential Equations by Charles E. Roberts, Jr. CRC Press. 2010
Section: Chapter 2. The Initial Value Problem. Exercises 2.3.2, page 63
Problem number: 8.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_separable]
\[ \boxed {y^{\prime }-y x=x} \] With initial conditions \begin {align*} [y \left (1\right ) = 2] \end {align*}
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 17
dsolve([diff(y(x),x)=x*y(x)+x,y(1) = 2],y(x), singsol=all)
\[ y \left (x \right ) = -1+3 \,{\mathrm e}^{\frac {\left (x -1\right ) \left (x +1\right )}{2}} \]
✓ Solution by Mathematica
Time used: 0.099 (sec). Leaf size: 20
DSolve[{y'[x]==x*y[x]+x,{y[1]==2}},y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to 3 e^{\frac {1}{2} \left (x^2-1\right )}-1 \]