81.7.9 problem 10

Internal problem ID [18706]
Book : A short course on differential equations. By Donald Francis Campbell. Maxmillan company. London. 1907
Section : Chapter VI. Certain particular forms of equations. Exercises at page 74
Problem number : 10
Date solved : Tuesday, January 28, 2025 at 12:12:05 PM
CAS classification : [[_2nd_order, _missing_y]]

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

✓ Solution by Maple

Time used: 0.002 (sec). Leaf size: 21

dsolve(x=diff(y(x),x)+diff(y(x),x$2),y(x), singsol=all)
 

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

✓ Solution by Mathematica

Time used: 0.036 (sec). Leaf size: 27

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

\[ y(x)\to \frac {x^2}{2}-x-c_1 e^{-x}+c_2 \]