35.8.26 problem 26

Internal problem ID [6233]
Book : Mathematical Methods in the Physical Sciences. third edition. Mary L. Boas. John Wiley. 2006
Section : Chapter 8, Ordinary differential equations. Section 13. Miscellaneous problems. page 466
Problem number : 26
Date solved : Monday, January 27, 2025 at 01:49:36 PM
CAS classification : [_linear]

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

With initial conditions

\begin{align*} y \left (2\right )&=6 \end{align*}

✓ Solution by Maple

Time used: 0.004 (sec). Leaf size: 9

dsolve([x*diff(y(x),x)-y(x)=x^2,y(2) = 6],y(x), singsol=all)
 

\[ y = x \left (x +1\right ) \]

✓ Solution by Mathematica

Time used: 0.029 (sec). Leaf size: 10

DSolve[{x*D[y[x],x]-y[x]==x^2,{y[2]==6}},y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to x (x+1) \]