81.6.4 problem 4

Internal problem ID [18687]
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 : 4
Date solved : Tuesday, January 28, 2025 at 12:10:24 PM
CAS classification : [[_3rd_order, _with_linear_symmetries]]

\begin{align*} x^{3} y^{\prime \prime \prime }+2 x^{2} y^{\prime \prime }-4 x y^{\prime }+4 y&=\ln \left (x \right ) \end{align*}

✓ Solution by Maple

Time used: 0.006 (sec). Leaf size: 23

dsolve(x^3*diff(y(x),x$3)+2*x^2*diff(y(x),x$2)-4*x*diff(y(x),x)+4*y(x)=ln(x),y(x), singsol=all)
 

\[ y \left (x \right ) = \frac {\ln \left (x \right )}{4}+\frac {1}{4}+c_{1} x +\frac {c_{2}}{x^{2}}+c_3 \,x^{2} \]

✓ Solution by Mathematica

Time used: 0.007 (sec). Leaf size: 30

DSolve[x^3*D[y[x],{x,3}]+2*x^2*D[y[x],{x,2}]-4*x*D[y[x],x]+4*y[x]==Log[x],y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to c_3 x^2+\frac {c_1}{x^2}+\frac {1}{4} (\log (x)+1)+c_2 x \]