81.6.6 problem 6

Internal problem ID [18689]
Book : A short course on differential equations. By Donald Francis Campbell. Maxmillan company. London. 1907
Section : Chapter V. Homogeneous linear differential equations. Exact equations. Exercises at page 69
Problem number : 6
Date solved : Tuesday, January 28, 2025 at 12:10:25 PM
CAS classification : [[_2nd_order, _missing_y]]

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

✓ Solution by Maple

Time used: 0.001 (sec). Leaf size: 17

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

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

✓ Solution by Mathematica

Time used: 0.027 (sec). Leaf size: 22

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

\[ y(x)\to \frac {x^2}{3}-\frac {c_1}{x}+c_2 \]