35.2.10 problem 10

Internal problem ID [6102]
Book : Mathematical Methods in the Physical Sciences. third edition. Mary L. Boas. John Wiley. 2006
Section : Chapter 8, Ordinary differential equations. Section 2. Separable equations. page 398
Problem number : 10
Date solved : Monday, January 27, 2025 at 01:36:13 PM
CAS classification : [_separable]

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

With initial conditions

\begin{align*} y \left (0\right )&=1 \end{align*}

✓ Solution by Maple

Time used: 0.008 (sec). Leaf size: 14

dsolve([diff(y(x),x)-x*y(x)=x,y(0) = 1],y(x), singsol=all)
 

\[ y = -1+2 \,{\mathrm e}^{\frac {x^{2}}{2}} \]

✓ Solution by Mathematica

Time used: 0.071 (sec). Leaf size: 20

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

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