15.16.13 problem 13

Internal problem ID [3233]
Book : Differential Equations by Alfred L. Nelson, Karl W. Folley, Max Coral. 3rd ed. DC heath. Boston. 1964
Section : Exercise 25, page 112
Problem number : 13
Date solved : Monday, January 27, 2025 at 07:27:11 AM
CAS classification : [[_3rd_order, _with_linear_symmetries]]

\begin{align*} 4 x^{3} y^{\prime \prime \prime }+8 x^{2} y^{\prime \prime }-x y^{\prime }+y&=x +\ln \left (x \right ) \end{align*}

✓ Solution by Maple

Time used: 0.007 (sec). Leaf size: 29

dsolve(4*x^3*diff(y(x),x$3)+8*x^2*diff(y(x),x$2)-x*diff(y(x),x)+y(x)=x+ln(x),y(x), singsol=all)
 

\[ y = \frac {x \ln \left (x \right )}{3}+\ln \left (x \right )+1-\frac {8 x}{9}+c_{1} x +\frac {c_2}{\sqrt {x}}+c_3 \sqrt {x} \]

✓ Solution by Mathematica

Time used: 0.023 (sec). Leaf size: 40

DSolve[4*x^3*D[y[x],{x,3}]+8*x^2*D[y[x],{x,2}]-x*D[y[x],x]+y[x]==x+Log[x],y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \frac {1}{3} (x+3) \log (x)+\frac {c_1}{\sqrt {x}}+c_2 \sqrt {x}+\left (-\frac {8}{9}+c_3\right ) x+1 \]