71.6.8 problem 8

Internal problem ID [14414]
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
Date solved : Tuesday, January 28, 2025 at 06:30:11 AM
CAS classification : [_separable]

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

With initial conditions

\begin{align*} y \left (1\right )&=2 \end{align*}

✓ Solution by Maple

Time used: 0.022 (sec). Leaf size: 17

dsolve([diff(y(x),x)=x*y(x)+x,y(1) = 2],y(x), singsol=all)
 

\[ y = -1+3 \,{\mathrm e}^{\frac {\left (x -1\right ) \left (x +1\right )}{2}} \]

✓ Solution by Mathematica

Time used: 0.061 (sec). Leaf size: 20

DSolve[{D[y[x],x]==x*y[x]+x,{y[1]==2}},y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to 3 e^{\frac {1}{2} \left (x^2-1\right )}-1 \]