81.7.8 problem 9

Internal problem ID [18705]
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 : 9
Date solved : Tuesday, January 28, 2025 at 12:12:03 PM
CAS classification : [[_2nd_order, _missing_y]]

\begin{align*} x y^{\prime \prime }+3 y^{\prime }&=3 x \end{align*}

✓ Solution by Maple

Time used: 0.002 (sec). Leaf size: 17

dsolve(x*diff(y(x),x$2)+3*diff(y(x),x)=3*x,y(x), singsol=all)
 

\[ y \left (x \right ) = \frac {3 x^{2}}{8}-\frac {c_{1}}{2 x^{2}}+c_{2} \]

✓ Solution by Mathematica

Time used: 0.027 (sec). Leaf size: 24

DSolve[x*D[y[x],{x,2}]+3*D[y[x],x]==3*x,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \frac {3 x^2}{8}-\frac {c_1}{2 x^2}+c_2 \]